You have still completely missed/ignored my main point, so I will ignore everything else and focus on this.

You have 2 combos, the job of both is to do damage. This creates a conflict of interest where the 2 combos fight for the same spot. These combos are as follows:

Fast Blade > Riot Blade > Royal Authority which gives 3 Sword Oath and 1 Divine Might

Fast Blade > Riot Blade > Atonement which gives 2 Sword Oath stacks and 2 Divine Might

The potencies are as follows as pulled from your posts:
Fast Blade 200 potency (300 under Sword Oath)*
Riot Blade 250 potency (300 under Sword Oath)*
Royal Authority 300 Potency, no buff under Sword Oath
Atonement 300 potency under Sword Oath
Holy Spirit 380**

*You never provided a potency for Fast Blade, so I will use the current potency and the potency you used for Riot Blade doesn't match current potency, however neither of these change the outcome.
**You listed a potency for Holy Spirit, however, as far as I can tell, this was not specified whether it was the base potency or the one under Divine Might. Either way, the outcome does not change. You also listed listed it as 390 potency and stated that it could be either or based on balance.

To measure the effectiveness of each combo, we will look at the average potency of each combo per GCD under different scenarios and see which one is best:

Case 1: Only Royal Authority combo, no Sword Oath buffs to combo. This will look at the combo potency for using the Royal Authority combo over and over whilst using Sword Oath stacks to use Atonement out of combo.

Fast Blade > Riot Blade > Royal Authority > Atonement Atonement > Atonement > Holy Spirit

200 + 250 + 300 + 300 + 300 + 300 + 380 = 2030 potency over 7 GCDs which gives an average of 290 potency per GCD.

Case 2: Only the Atonement Combo, no Sword Oath buffs to combo. Same as above, just with the other combo.

Fast Blade > Riot Blade > Atonement > Atonement > Atonement > Holy Spirit > Holy Spirit

200 + 250 + 300 + 300 + 300 + 380 + 380 = 2110 potency over 7 GCDs which gives an average of 301.4 potency per GCD.

Case 3: Same as case 1, however, using the Sword Oath stacks to buff the next combo. I will take the 2 Sword Oath stacks from Royal so that only 1 Atonement is used out of combo.

SO Fast Blade > SO Riot Blade > Royal Authority > Atonement > Holy Spirit

300 + 300 + 300 + 300 + 380 = 1580 potency over 5 GCDs which gives an average of 316 potency per GCD.

Case 4: Same as above, just with the Atonement combo. I have made the assumption here that, if comboed off of Riot Blade, Sword Oath is not required at all and still retain full potency.

SO Fast Blade > SO Riot Blade > Atonement > Holy Spirit > Holy Spirit

300 + 300 + 300 + 380 + 380 = 1660 potency over 5 GCDs which gives an average of 332 potency per GCD.

Case 5: Alternating, Royal > Atonement. In total you gain 5 Sword Oath stacks, 4 of which are used to buff combo actions which leaves 1 to use on its own. You also gain 3 Divine Might Stacks.

SO Fast Blade > SO Riot Blade > Royal Authority > Atonement > SO Fast Blade > SO Riot Blade > Atonement > Holy Spirit > Holy Spirit > Holy Spirit

300 + 300 + 300 + 300 + 300+ 300 + 300 + 380 + 380 + 380 = 3240 potency over 10 GCDs which gives an average of 324 potency per GCD

As we can see, the strongest combo to do is spamming the Atonement combo using Sword Oath to buff the combo starter. The reason is because of the increased Holy Spirits you have. Now, whilst I have labelled these as using the Holy Spirits right after, you can move these around however you want in the combos, or delay their use to use whenever you want, as long as you do not overcap the 5 stack limit IIRC you mentioned.



Next comes how it will play out. You will notice in the above calculations I omitted the fact that you potentially needed a Sword Oath stack in order for the comboed Atonement to give you 2 Sword Oath stacks, which would leave you at 3 stacks after, which leaves room for another naked Atonement, this just brings up the potency to 326.7 potency per GCD over 6 GCDs. With this in mind, I want to compare 2 rotations, one with that constraint in mind and one where it doesn't. They will both come from an opener as follows:

Shield Bash > Goring Blade > Holy Spirit > Confiteor > BoF > BoT > BoV ... After this, assuming both Goring Blade and BoV give the same effects in regards to Royal Blessing (+30 seconds to a max of 60s), this leaves a time remaining of 47.5 seconds, which means the next Goring Blade has to come in the next 7-19 GCDs for no loss, then, as long as BoV comes at the same time, there will be no worry of loss.

So, with the constraint that you need a SO buff to get the extra ones from a comboed Atonement, we can construct the following (from now on, all SO buffed GCDs will be underlined, buffs will be tracked as follows [SO|DM])

Fast Blade > Riot Blade > Royal Authority [3|1] > Fast Blade [2|1] > Riot Blade [1|1] > Atonement [3|3] > Holy Spirit [3|2] > Shield Bash [2|2] > Goring Blade [1|3] > Fast Blade [0|3] > Riot Blade [0|3] > Royal Authority [3|3] > Fast Blade [2|3] > Riot Blade [1|3] > Atonement [3|3] > Fast Blade [2|3] > Riot Blade [1|3] > Atonement [3|5] > Holy Spirit [3|4] > Burst etc.

Some observations. Using the Atonement combo means you can use the Atonement combo again without worry, unless you need to refresh Royal Blessing, in which case your next combo has to be the Royal Authority one in order to get the necessary stacks. This means, past the opener, you will only use the Royal Authority combo once per minute and only after Goring Blade, I'm sure this was not your intent, however, that is how it is playing out. If you change it so that BoV does not give you Royal Blessing, then Goring Blade has to be applied at the latest at the first Holy Spirit in the above, which means, after the burst, it will look something like Royal Authority > Goring Blade > Royal Authority. It should be the same resources at the end going into burst (not actually checked), however the next section of rotation will be all Atonement combos.

The next thing to comment on is coming up to the burst. knowing what to do with the last few GCDs, Do I have enough time to get another Atonement combo in, will this cause me to overcap on Divine Might, if I cannot afford that, do I have the resources to delay the rotation with Holy Spirit or, Atonement? Or do I not and so risk losing a Holy Spirit in burst because of it. I haven't worked past the first minute, however, these are potential problems that could arise.

If we do the same except allow the case where SO is not needed to get the 2 stacks,

Fast Blade > Riot Blade > Atonement [2|2] > Holy Spirit [2|1] > Fast Blade [1|1] > Riot Blade [0|1] > Atonement [2|3] > Holy Spirit [2|2] > Shield Bash [1|2] > Goring Blade [0|3] > Holy Spirit [0|2] > Fast Blade [0|2] > Riot Blade [0|2] > Atonement[2|4] > Holy Spirit [2|3] > Fast Blade [1|3] > Riot Blade [0|3] > Atonement [2|3] > Holy Spirit [2|2] > Burst

Now, I don't know if you were playing along, however, it was much easier to determine how to effectively enter the burst phase as there is less to track. There is of course the same issues here as there was before, however, I would say it is much better managed here as resources are more consistent.

However, lets talk about the idea as whole. The first thing I can tell you, without even doing any calculations is that the second rotation will do more potency than the first and I can say that for one simple reason, it has more Holy Spirit casts. The reason I can say that for certain is down to, what I perceive anyway, a fundamental flaw in the Sword Oath idea as a whole. With the exception of Goring Blade, everything becomes Atonement/Royal Authority potency, with the odd one here and there being less. Which brings us back to Royal Authority. With it basically being a gateway into the higher damage Sword Oath combo, I don't think it would feel rewarding to use, it acts more as a hurdle to your damage than something that rewards you with damage. I couldn't find the words to properly express the feeling, however I hope that gives an idea. Goring Blade is already a hurdle you need to get past to do your damage, so why add another one. Then, with 2 combos being virtually identical, people will ask, what is the point? Might as well just combine them, of which the next question would be, what is the point of all this Sword Oath nonsense. Pretty much everything is buffed with it anyway, so why bother? Both of these are points of frustration and could be perceived as clunk, which is never a good thing. I am also aware you have mentioned Circle of Scorn using Sword Oath to buff itself, which is just a bad idea and adds unnecessary restrictions to the usage.

With everything said and done however, you essentially have 2 rotations to choose from, one is the one you proposed and how I see it playing out and the other is basically what we have now admittedly. Both of them however add in that short combo to make PLD just that much closer to Warrior, it is just that one of them (in my opinion) has much more clunk and is far more restrictive/less intuitive than the other one and I could see PLD losing even more players from it.

Also, to counter your burst damage, I have no idea where you suddenly pulled a potency number from, however, here are the facts:

Highest Burst (2 Divine Might Holy Spirit), 6600 potency after FoF, 8 GCDs, you can get 2 full combos in, for 2130 total potency each, over 7 GCDs, that leaves 2 slots, so add Fast Blade and Riot Blade to give the burst as much power over the total potency as possible.

Add it all up (6600 + 2130 + 2130 + 200 + 280) = 11340 potency over a minute, 6600 of that is burst potency, 4740 is filler potency. If you calculate how much higher the burst is (6600 / 4740) you get 1.3924....... or, in other words, the Burst potency is just less than 40% higher than the filler potency and this is trying to give the burst as much as possible. This lines up with what you read that the burst should be no more than 40% of the jobs damage.