I believe the "problem" with the Warlord concept is it should have never been giving healing powers as that steps all over the cleric prime ability. If the warlord gives out THP that's a different story and more appropriate to the theme and concept.
The 4e warlord didn't step over the cleric.
It's healing was only ever healing surges (hit die) + bonus. Where a cleric got flat healing.
Specifically, it was.
Inspiring Word
Minor action
Burst 5 (Burst 10 at level 11, and burst 15 at level 21)
The target can spend a healing surge. If the target does so, he or she regains 1d6 additional hit points.
Level 6: 2d6 additional hit points
Level 11: 3d6 additional hit points
....
You can use this power twice per encounter. But only once per round"
So adjusting to 5e's numbers, style, and hit dice, you would get...
Inspiring word:
As a bonus action, you can let an ally with 20' spend a hit die. If the target does so, they regain an extra 1d4 hit points. You can use this feature twice per short rest.
At level 5, they can spend 2 hit dice and gain a 2d4 bonus. The range increases to 30'.
At level 11, they can spend 3 hit dice and gain a 3d4 bonus. You can use this power 3 times per short rest.
At level 17, they can spend 4 hit dice and gain a 4d4 bonus. The range increases to 40''
Inspiring Warlord sub-class.
...
Level 6: When you use Inspiring word, you can add your Charisma modifier to the amount healed.