I still think (non magical) temporary hit points may be an option and compromise here.
Can't bring PCs up from unconsciousness.
Part of the problem is that the objections people have to Inspiring Word are at a level of granularity that doesn't exist in D&D. D&D doesn't distinguish between different ways of inflicting damage, you just lose hps, it doesn't differentiate between different ways of restoring hps, either. A solid mechanical solution would mean increasing granularity - with two or more different 'pools' of hps or with different types of hp restoration working at different efficiencies against different types of damage, and/or with a third form of hp-granting beyond temps and hp-restoration.
The problem I have with "compromises" like this is that one side still gets 100% of what they want while the other side has to accommodate.
You have to take into account that this would not be a compromise between wanting an optional, balanced, faithful rendition of the Warlord on one side, and wanting the Warlord erased from D&D for all time on the other, but rather a compromise between two equally unreasonable extremes.
Those extremes would seem to be:
[sblock="realize, I AM trying to make these sound extreme and unreasonable, so brace yourself"]
The warlord must be errata'd into the 5e PH, be made mandatory in AL play, and be designed as a wildly-overpowered class that completely dominates play, and renders all other support classes obsolete, so that all parties are faced with the choice of having a warlord in the party, or being non-viable by comparison. The Warlord must include powers that are nominally non-magical, but strictly superior to everything Clerics, Druids, Bard, Paladins, & Rangers can do (combined). Most of these powers should function via a 'plot coupon' mechanism that completely re-writes the events of the game and nature and motivation of allies, enemies, and NPCs alike, rendering the DM impotent. These powers must include the ability to literally shout wounds closed, including resurrecting the dead, and shouting away conditions, curses, diseases, missing limbs, or any other negative effects allies must be suffering form (apart from that feeling of inferiority that comes from being under the command of a Warlord, of course). Which reminds me, though it should go without saying, in any party containing a Warlord, the Warlord is party leader, and the player of the warlord totally gets to boss everyone around, DM not excepted.
vs
The warlord must not exist in D&D in any form, the OGL must include a 'no warlords' clause, and WotC must sue anyone who makes a warlord publically available. WotC must also recall & destroy any past publication containing or referring to the Warlord, as well as taking down any on-line content or references related to it. The definition of 'Warlord' for these purposes extends to any martial class that doesn't suck.[/sblock]At least, to judge by the fears expressed by either side.
Real compromises on the healing issues, well inside the vast common ground between those two extremes, have been articulated up-thread, and in the How many fans want a 5e Warlord thread, if you're willing to dig for 'em...