Yes, it would surely require co-operation from both the FA and the PL - between them deciding how to implement this within the dishing out of Sky's millions* - for the idea to even get off the ground. But it would appear that the PL have little interest in co-operating.
*For example, rather than set additional prize money aside to reward a club for finishing, say, 11th rather than 14th, pay them the same and put the money saved into this new pot....Basically splitting the pot into four parts rather than three (as far as I am aware, at present, roughly 1/3 is distributed based on final league position, roughly 1/3 is based on number of times you're televised, and roughly 1/3 is split equally between all 20 teams, seemingly just for being a PL club).