I would seriously recommend NOT doing it. The clear coat isn't "integrated" into anything. What you have is a very basic single-stage paint job.

Single-stage is very hard to buff to any decent shine and if you burn the paint you've ruined your paint job, regardless of how cheap it was it still sucks that it now is screwed.

My two cents says to just deal with the fact that you were a cheap ass and got what you payed for.