Just gonna comment on some of the OP's suggestions.
Make Darkside, Sword Oath, and Deliverance stances use Parry. Let me explain --- what if changing to the aforementioned stances also increased damage with the aid of Parry? Let’s say, when in Deliverance stance, reduce 30% of Parry stat and increase attack power by say (0.01 x reduced parry) %. For Darkside, increase Crit Rate by 10% of Parry. For Sword Oath, a flat damage and accuracy increase by 5% of Parry. This change may eliminate other classes wanting to abuse Parry changes by equipping fending accessories
While this is a good idea, I am slightly bugged by the fact that in order to make a defensive stat be "not bad" you have to turn it into an offensive/damage stat in some way. That said, I'd probably change the stat's name to Composure or Expertise if we were to go down this route.
Make Parry reduce magical damage as well. I can see why this could be a problem for what the developers intended, so I would understand if this one is not considered, which brings me to my next suggestion:

Give a trait to Dark Knights to make their Parry mitigate magical damage as well. The meta that we see right now for Dark Knights is that they are chosen for magic-heavy battles. This trait will just make them fit the mold better.
The devs have a weird aversion to having mitigation work on magic. I'm not sure on whether it's because they think it's overpowered or for thematic reasons, but they've already shot down shield blocks working against magic, so I'd guess parries are out as well.
Make Parry counter damage. Similar to MRD/WAR’s Vengeance skill, what if tanks return the flat 20% reduction as damage? Vengeance would still be useful as it still has the 30% reduction + 50 potency return for every physical damage. What if Parry returns 5% of its stat in potency to every kind of damage?
You mean a passive "spikes" effect that procs on parries? That might be a nice a passive bonus to it.

An alternative would be to have parries reduce/reset the swing timer for your auto attacks for 1-2 seconds. This way you are basically attacking as a result of the parry.
Change Parry to be additive to Defence/Magic Defence stat. This is the lazy change to the Parry change. If SE really wants to stick to the meta, they might go: WAR: 7.5% of Parry is added to physical and magical defence. PLD: 15% of Parry is added to physical defence. DRK: 15% of Parry is added to magical defence.
On the one hand, you could create a tank trait that grant these effects. On the other hand, you once again might as well change the stat's name if you're going there.
Note that I am not even including the pre-Heavensward Parry state --- the suggestions above work with the developers’ decision to stick to what Parry does right now. I just made suggestions based on Parry’s inherent issues. What would you suggest to Square Enix?
Personally, I'd like them to remove the stat as a whole from gear and replace it with a stat that either encompasses more things (sort of like a general defense stat that increases damage mitigation, parry and block rates by a little) or just replace it with crit/acc/skill speed/det on the appropriate pieces of gear.

Then have classes work with parries on an as-needed basis. Design a new job that can manipulate their parry rate via abilities/buffs/combo bonuses to start and go from there.

Calling the trait Parry and keeping it in the game would require (as far as I can tell) a revamp of mitigation tools for all tanks and how much control they have over said tools. Right now a tank has no control over mitigation between Parry's terrible scaling, the fact dodge rates are fixed values and blocks are equally fixed.