Yes, I suppose hit dice would make sense. Like every hit dice used (maybe a max of 3), acts as a charge on a Soul Coin. This would also allow the use of a sometimes under utilized resource.
Maybe rolling above a certain number on the hit dice could function like applying demon ichor to the engine. Not sure if I want it to be max though as that would reward low hit dice characters like Wizards while making it tricker for higher hit dice class like Barbs and Fighters to apply the ichor bonuses.