I wonder if you could remove the seat, turn it over, and dig it out from the inside... I've never messed with a seat before... but the padding is pretty thick. Would it still be comfortable with about half of the padding it has now?
Hard to explain what I'm thinking... but if you could build a seat pan that was elevated by an inch, maybe two, and empty underneath...then you could stretch the seat cover back down over the elevated pan, so that it looked stock but had some extra height underneath...
I don't have the skill, but others here do for sure