The "until it leaves play" part I think is already known just by the rulings on things like Throne Room BoM without any Overload interactions. If you Throne Room a BoM, and choose a Feast, then it has been ruled (more recently), that when BoM-Feast gets trashed, it reverts to BoM so you can choose anything else. At that point, whatever you choose, you get to play it for the effects, but it never gets into play, so BoM stops being it the same moment it becomes it.
The only difference here is that we care about cost. I think "costing less than this" must be "costing less than this currently costs", so...
-Play Throne Room, choose Overlord.
--Play Overlord first time
---Choose Feast
---Play Overlord as Feast
---Gain a card, trash Overlord (Overlord cost briefly becomes
and then goes back to
--Play Overlord second time
---Choose Band of Misfits
---Play Overlord as Band of Misfits
---Choose a card costing less than this (this is the card you are playing, it costs
---You can choose any card costing only
and no
, with a debt cost less than
.