You should be asking your LCD supplier those questions.

You should also consider how much time & effort it is going to take you to develop this from scratch with no prior knowledge or experience.
Is it worth it?
Do you want to become an EL power supply expert?

It is perfectly feasible these days to design your very own microcontroller & implement it in an FPGA - so why are you happy to buy an off-the-shelf microcontroller, but not an off-the-shelf EL power supply?