Is there? Well, if there's a lot of incoming damage there might be. But you're right about Syn not affecting Dig, as Dig is an ability (not a spell) the secondary benefit of Synastry doesn't happen. I double checked the tool-tip and even went through verifying IG just to be sure (xivdb just says it's was a skill, not whether it's a spell or an ability). Also, while looking into this, it appears that Dig likewise does not get the benefit of +5% from Noct. Which is disappointing, but also good to know.
And no, while not exclusive, the DiAst will probably prioritize their regens when Synastry is up to get stronger ticks. I can see A. Helios followed up by Benefic and then A. Benefic for tanks. The NoctAst, on the other hand, should prioritize the normal Helios before going on to Benefic and Benefic II which would get a party up faster, and cheaper. This is, of course, as one other person in this thread pointed out, front-loading your heals.
Taking a DiAst and a NoctAst in the same scenario, paired with a SCH, it's easy to assume the DiAst will stick to their guns and roll their regens while the SCH shields. They'll then move on to handle whichever mechanics they need to, as appropriate. As stated numerous times, and not once refuted by me, this is good. There's a synergy there, and that's obvious. The NoctAst, meanwhile, doesn't prioritize their shields, and instead prioritizes Benefic or Benefic II.
Continuing to run with this scenario, we can assume that because the AST in both cases used an AoE heal, the SCH might also have to use their own AoE. They can either choose to use Succor (150potx2), Eos's Whispering Dawn (100pot over 21sec, 7 ticks for 700pot total per target) or if necessary both. For funzies, we'll go with both.
In the case of the DiAst that becomes a beginning potency of 350, with a shield of 150, and regen of 140 every tick for 21sec (total 980) and then another 40 for 6sec (or 80 total) before regen have to be reapplied.
In the case of the NoctAst that's a potency of 525, with a shield of 150, and regen of 100 every tick for 21 sec (total 700).
It takes another 3sec before regens catches up, and then another 3sec before surpassing. After that initial 6 seconds, however, Diurnal undoubtedly beats out Nocturnal in HPS for obvious reasons. A NoctAst cannot compete in a HPS game, as after the first tick (870 start + 180/tick for 18sec vs. 1375 flat) they start losing.
If your goal is high HPS, congratulations. You have the highest HPS in a contest that was a no brainer.
Back tracking a bit, so we have a context for all the above math.... We already know how well the AST(di)+SCH interact; that is, very well. They compliment each other almost as well as WHM+SCH, because that's what its like. Opposite of it, we have the AST(no)+SCH which we don't know how good/bad this combination is. We only know it's not optimally preferred, and no one wants to try it out. People are all too ready to dismiss the combo, mainly because the expect another round of SCH+SCH, when it's not exactly that. It'll be similar (like it is in the case with Diurnal+SCH) in that one person will be shielding (SCH) and the other person will..., well, not be shielding.
Unlike the SCH+SCH combo, the AST isn't shoe-horned into summoning Selene (who has a 1sec silence, and a 30sec buff to Spellspeed or Skillspeed) and not using their Adlo or Succor (or other similar abilities which might not stack). Instead, they've got: comparable healing; buffs for mitigation, recast timers, damage, attack speed, mp regen, or tp regen; a quicker/cheaper way to handle people who've just been rez'd (lightspeed + stoneskin + protect all in 5sec and party is good to go); an extension for their buffs; an extension on buffs in general; damage mitigation+regen to go with their co-healers damage mitigation/regen.
Maths:
Di Benefic 480
No Benefic 500
Di Helios 360
No Helios 375
Di A. Benefic 190 + 840 (over 18sec, 6 ticks)
No A. Benefic 250 + 325 (lasting 30sec, expect 2-3sec on a tank)
Di A. Helios 200 + 400 (over 30sec, 10 ticks) per target
No A. Helios 150 + 150 (lasting 30sec, mileage may vary) per target
Feels like it, I know, but it's not. Less 2+2=/=5 and more a+c=/=a.
Honestly, until I can make a run with the NoctAst+SCH combo, I don't expect to find much in comparing the other combinations aside from what's already been found. What I do expect is to engage others in healthy conversation (or try to) where I explain myself, and those that want to continue the conversation can.
The original hypothesis was made prior to the changes to AST, and worked under the assumption that AST might not be given buffs to make them comparable to the other two healers. I made a guess that the intent behind the AST design was to mimic the other two healers to capitalize on the other healer's strengths, without stepping on their toes but still allowing the players to decide how and when to play in each sect. Prior to 3.07 trying to be a WHM in Diurnal was a struggle, and SCH in Nocturnal laughable, so I made an assumption and asked the community to help me figure out if it was viable/possible. Instead, what I got was a lot of people not willing to take a little time out of their gameplay to at the very least try something different.
I asked, very simply, for someone (anyone, really) to try, and come back with what I expected was a "sorry, man, it just doesn't work and here's under what circumstance and why".
Instead we've spent the last 5 weeks talking about why no one wants to try. When it would have taken one run-through of any two of the Alexander floors (one where the healing wasn't so intense, and another where it was) and this whole thread could be put to rest. Not only would that give us, the players, feedback about where the NoctAst is lacking when paired with SCH, but an easy reference for new players who might have the same question and not be satisfied with the "because diurnal is like whm and therefore better."
That's not saying I haven't seen some very good explanations as to why it might not work well, because I have and that's fine. I'm happy to see those types of responses as they explain what types of difficulties the pairing will likely run into, but that's all it does. It explains why it might, and doesn't show why it does.