Now that I'm not working on mine at the moment (
shameless plug 
) I have time to reflect on yours. I mostly feel like you need to reword your stuff so it is more in line with the rest of 5e. In particular, you need to use the second person 'you' instead of 'the warlord'. Also you need a ribbon ability early on and possibly a tool proficiency.
The warlord must be interacting with either the ally using their reaction or their target (often as a distraction) to use this ability.
What does 'interacting with' means in this case?
Inspiration
The Warlord may use their bonus action to enable an ally to dig deep into their reserves and grit through things. One ally they are interacting with (including shouting at) may spend a hit dice plus a further one for every four full levels they have, and the hit points recovered are maximised. This ability is recharged on a short rest.
This is another case of messy wording. The 'four full levels' thing in particular is needlessly fiddly. Just say at which level they can spend an extra hit dice.
Fighting Style
The Warlord can choose any fighter fighting style. In addition they may pick from the Warlord fighting style list:
- Spotter: When the warlord uses Set-Up allies may use ranged attack against foes distant from the warlord.
- Mystical Set-up: Cantrips may be cast as a response to set-up. Note that ranged cantrips also require the Spotter style unless the target is in melee with the warlord
- Smooth teamwork: When benefiting from Set-Up actions that do not involve spellcasting no longer use up reactions. An ally may not get two extra actions from Set-Up on the same turn however.
I think the Warlord shouldn't get ALL the Fighting styles. They should get Defensive, Protection, maybe Archery, the one that grants maneuvers from the UA, maybe one of the cantrip granting ones and then the new ones for Warlord. You're also missing the bit about not getting a fighting style twice.
Spotter is a bit messy, wording wise, but it's a good principle. Mystical Set-up seems unnecessarily long, just say that in response to set-up the ally can use a Cantrip in place of a ranged attack and let the rules of Set-Up apply as normal.
Smooth Teamwork feels more like a later feature than a fighting style.
Bastion
Beginning at 9th level, as a reaction you can allow all allies who failed a save against one effect to reroll their saving throws. If they do so, you must use the new roll, and you can't use this feature again until you finish a long rest.This has no effect on what you rolled.
You can use this feature twice between long rests starting at 13th level.
At what range exactly? Do you also have to be the target of the effect to allow your allies to benefit from it? It's a good support effect but could use further clean up of the wording.
Delegation
At level 20 the Warlord is sufficiently legendary that they don’t even need to be physically present to run combat like a well oiled machine. Any group of close allies that the warlord trusts (current or former adventuring comrades are close enough to qualify) may treat the warlord as if they were physically present and using an action on Set-Up every round on Initiative 15 as long as they are either (a) following a plan the Warlord contributed significantly to or (b) working directly in the best interests of their warlord ally.
The idea is fantastic in terms of concept but I'm not sure on how it would work out in play. It seems a bit too limited since it hinges on splitting the party.
I'll check the subclasses later.