I think the OP for this thread should have been presented in a 'trade offer meme' format. Sure, you'll 'grudgingly' take an upgrade to Thrill of Battle that renders it superior to Dark Mind virtually all conditions, just like Shake it Off is superior to Dark Missionary under virtually all conditions. And all in exchange for making WAR healing actually follow the stated text description and become a bit less broken in AoE. What a deal.
This is what you actually need to do.
Removing Invulns
First, you need to get rid of all tank invulns. A three minute recast variation between tank invulns is grossly imbalanced, and you honestly shouldn't have to fall back on them in fights with 4-5 tankbusters. SE has repeatedly proven that they are unable to balance tank invulns, much like they repeatedly proved that they couldn't balance tank stances prior to them being made vestigial. It's time for invulns to go. They're also very quickly running out of unique drawbacks for these, so if a new tank gets introduced in 8.0, they're better off scrapping the concepts altogether (and possibly just replacing them with a tier of big, non-invuln mitigations).
Rebalancing Raidwide Mitigation
Next, you look at the raidwide mitigation buffs. Either they all operate on conditional damage types (i.e. Shake it Off works on physical damage only), or none of them do.
It's also worth noting that even on a fight with magical damage, in order for Dark Missionary or Heart of Light to just break even with Shake it Off, the incoming magical raidwide damage over 15 seconds needs to exceed anywhere from 150% to 190% of your WAR's total HP. And that's before we look at the heal and regen effects built into it.
Hotfixing Bloodwhetting and Nascent Flash
Both Bloodwhetting and Nascent Flash specifically state in the tooltip that they restore HP with each weaponskill successfully delivered. That should be the heal potency per action, not per hit.
Future Directions
I think if you address these three points, you'll put an end to most of the role encroachment concerns and balance concerns raised around WAR. The focus needs to shift back towards skillful execution of defensives to survive. Replace passive healing and regen effects baked into the rotation with active, judicious use of sustain effects that require good timing and an understanding of incoming damage. Perhaps incorporate a theme around temporary HP effects where you try to boost your HP totals to absorb incoming damage, as was the case historically.
Either way, the current design approach is not sustainable and will drive players out of the role in the long run.