Are we overthinking the warlord?

[Tony Vargas]

It takes up to two days to recover all of your HD, and you one get one per level. Additionally, it's the same resource that short rest healing consumes.

Yep, that's the idea. HD are a natural (two) daily resource limit. Instead of mildly bizarre daily limits on being inspiring, HD can represent the finite nature of those deep reserves said inspiration exhorts you to call upon.
Comparatively simple & elegant, really. Even if only in comparison to neo-Vancian casting...

 

[Zardnaar]

Triggering and adding a bonus or matching dice to the HDs spent could work. The daily budget is still there, basically 1/2 HD since that's the rate at which they recover, but only the bonus or matching die counts toward the theoretical 'budget.'

As a bonus, large or small parties or multiple warlords don't distort the dynamic...

I went with grant second wind type thing over hit dice because it scales with level and it's simpler it's always a d8.

If you go with HD make them bonus ones. There's not enough of them. Very similar but I think I have figured out a way to scale it with level without spellslots.

 

[Cap'n Kobold]

One of my Warlord hacks was based around superiority dice, with a little bit of Bardic Inspiration. While they could share their Second Wind to give actual healing, much of their 'healing-type support' came from using the Rally ability - as per Battlemaster, but they could spend more dice on it.
At higher level, they had the ability to use Rally and similar maneuvers as reactions, pre-empting the damage from an attack and so absorbing some or all of it before hit points were lost.

This 'pro-active healing' seemed to engender a very tactical style of play and mindset that fitted well with the class fantasy, rather than the more 'whack-a-mole' style that people speak of as the cleric's.

(Similarly while the tactician couldn't flat-out remove many magical conditions as the other healers can, they could use dice to give bonuses to save against them in the first place and improve the chance of breaking out of ongoing effects. Later they could force new saves against mind-affecting or illusory effects even when the target wouldn't normally be able to make additional saves to break out of them.)

 

[Tony Vargas]

Rally and similar maneuvers as reactions, pre-empting the damage from an attack and so absorbing some or all of it before hit points were lost.

This 'pro-active healing' seemed to engender a very tactical style of play and mindset that fitted well with the class fantasy, rather than the more 'whack-a-mole' style that people speak of as the cleric's.

(Similarly while the tactician couldn't flat-out remove many magical conditions as the other healers can, they could use dice to give bonuses to save against them in the first place and improve the chance of breaking out of ongoing effects. Later they could force new saves against mind-affecting or illusory effects even when the target wouldn't normally be able to make additional saves to break out of them.)

Whack-a-mole isn't the Cleric's style, it's an artifact of a game mechanic: heal-from-0. 4e also had that mechanic, and even though healing was more plentiful and powerful than in 5e, making healing an ally before he dropped less inefficient, it still often slid into that kind of mode.

Actually, 5e's massive-damage & don't-count-negatives rules also encourages whack-a-mole a little more than 4e's death-at-negative-bloodied value did, I suppose, a bit.

I went with grant second wind type thing over hit dice because it scales with level and it's simpler it's always a d8.

HD naturally scale with level. So you can have both the level of the Warlord, and the level of the target act as a limiter.