I think the Exploits are too locked in to the subclasses.
Also, there should be a lower level ability to grant an attack. Just give it restrictions. It's fine if the ability defines exactly what their attack looks like, even. The point is, the tactical benefit of letting the Barbarian clobber something instead of the Warlord stabbing the guy in front of them, or letting the ranger shoot the enemy mage, etc. It'd be easier if 5e had Basic Attacks, including for spellcasters, but the Warlord feature could simply define such a thing.
Basic attack. The character makes a weapon attack or spell attack, using the appropriate attack stat. This attack is never made with Advantage.
Weapon attacks are made as if you had taken the Attack Action, except that they do not benefit from the Extra Attack feature.
Spellcasters can either use one of their known cantrips, cast as if they were 1st level, or make a Basic Spell Attack, which deals 1d8 damage of any type the character can normally deal with their known cantrips, uses their Spellcasting Ability Modifier to attack and damage, and has a range of 60ft. Components are Verbal and Somatic.
Letting the Warlord do that instead of making an attack, as an Action, seems about right to me. I get that people don't want rogues getting extra Sneak Attacks, which is why I made Basic Attacks never have Advantage. Dual Wielders and Monks kinda get hosed, since they can't spend a Bonus Action to get their normal extra damage, but that's hard to help. Most of the time, the weapon user with the longest range or biggest damage die will be the best person to give an attack to.
I'd say that starting with this, and then giving limited access to full extra Action granting, or even just letting the attacker use a feature that would normally cost a Bonus Action as part of the attack, would work.
I don't think this should cost both the warlord's Action and the recipient's Reaction. What if you could use your Reaction when granted an attack, and instead of a Basic Attack, you get to attack as if you had taken the Attack Action, including stuff like having Advantage, or use your Reaction in place of a Bonus Action to modify your attack? Maybe as a level 5 improvement of the ability?