Something I plan on doing soon (hopefully tomorrow) is double check the actual heights of the original kit bridge to the one I got from Guitar Fetish. I suspect the GF bridge that I'm currently using is slightly taller that the kit bridge and thus is the underlying cause of my string height issue.

The GF bridge is much nicer and has individual string intonation settings, but it does have substantial meat underneath to hold the string ends and so the reason for overall additional string height.
The other alternative is change to a normal LP style bridge with a trapeze or a stop bar. There is plenty of room to do either...