Delirium says:
... I'm considering getting Henry to share his team's exclusive clue ...
Ha! Why am I not surprised. :)
Delirium says:
... while misleading him by 'sharing' a false lead in return. ...
That sounds like Mislead/Trick.
Delirium says:
... I think both would be rolled with Heart anyways, because of their past relationship? ...
Absolutely. About time you get to use your special Moves.
Delirium says:
... Would I need to roll for that? Would it be a trick and mislead, or persuade? ...
That answer would depend on two things: What you are trying to do (mechanical outcomes), but mainly what you actually do (the fiction).
Persuade seems a good fit for getting his clue off him, but remember that
Persuade an NPC only works on NPCs, and
Persephone is with Henry, so you may need to separate them before you can use that Move on him.
Mislead, Distract, and Trick can work on PCs as well, and may be a way to distract
Persephone while you work on Henry?
@Drgwen: Are you happy with this PCvPC action?