Ha, if only I could get Yoshi's ear! Regardless, I be interested to see any suggestion of how WAR would close the gap, because I don't see anything which would suggest a remote chance of meeting PLD. Anyway, just to clear out the self-healing method...
Seeking only survival (note that you'd lose aggro, lose your defensive cooldowns, and lose your interrupts all if you did this -- this is just dumping cooldowns for building Wrath in a 90s Berserk/Bloodbath cycle), a WAR can push about 11,500 post-crit healing potency per 90 seconds (based on a spreadsheet I set up some time ago). Endgame WAR built for STR should push near 1 damage per potency. 11,500 heal per 90s is 127.78 per second. In addition, you'd have around 7% average healing boost. At 1000 damage per second, that's 65.42 more from the healing bonus, or a total of 193.2 HP/s from increased heal and self-heals. We know that PLD has already won, because the extra mitigation from Shield Oath alone is 200 HP/s, then shield block advantage and PLD use of Bloodbath. After all that, you'd have PLD who is more durable, still has interrupts, and has superior survival cooldowns (Rampart and Bulwark). And if you didn't gather from the first sentence, this strategy is completely untenable for a Warrior -- you would put both yourself and your team in jeopardy by attempting it. A more realistic rotation is around 9500 healed per 90s, which is weaker but doesn't involve hanging your squishy arse on the line by abandoning all of your defensive CDs sans Foresight.
If I want to be more thorough, I can look at the available skills and tell you that none of them will make the difference. Mantra is 5% healing for 15 seconds per 120, which is hilariously bad. Featherfoot is roughly equivalent to Bulwark over the duration -- this is why I never mention Bulwark as an advantage for PLD. Haymaker provides an effect (Slow) which several party members already have, which can only be used on rare occasion due to reduced evasion rates in endgame dungeons, to which opponents build resistance, and to which many opponents are immune. Internal Release is good for boosting damage and drain, but is only a boost of 10% of base damage for 1/4 of the time -- I used it in the spreadsheet estimate.
Full-STR self-healing is actually how I recommended people play the job back when the 300/300% setup first leaked -- it seemed the mathematically-superior route. It thought it would make a lovely tank and and only a little bit weaker at the absolute limits of healing capacity. However, at the time, healing was half as effective as it is now, and that proffered a limit on enemy damage which was not unfair to WAR. I assumed that the design would be more focused on skillful evasion and teamwork rather than raw tank-and-spank efficiency, that neither tank would withstand a bout standing in one place with whatever enraged demigod showed up. Alas, that never came to pass. With that boost to HP healed and associated dungeon design which involves incredible damage rates, WAR cannot keep up -- we knew that to be WAR's weakness before Phase 4 began. Basically, WAR's design made good sense as a berserking monster with P3 healing. At the limits of healing, WAR would require more skilled play than PLD, but could go toe-to-toe any time. PLD would be preferred, but WAR would still work out with some adjustments. The new healing formula makes WAR comparatively weaker, and that's pretty much all there is to it. Again, WAR might have made up the difference with other interrupts or similar means of decreasing enemy damage output, but it's PLD who has these advantages over WAR, putting a few more nails in the coffin.