The first things to try (if you haven't):
*Adjust the 'Clean Sens' and 'Dist Sens'. Either from the input menu, or better yet the Rig Manager software. Just crank or lower that, see if things improve. (can be drastic, very important)
*Change cabs. Find a decent tone gain-wise you like, lock the amp section in Rig manager, and load other profiles to audition just their cabs.
*If high end fizz is an issue, add an eq, then LP down to 8k, or cut out 7k or 5k.
You're already this far in, consider picking up an audio interface for a few hundred $. Even if you end up returning or selling the Kemper, the audio interface is invaluable, has so much use for home recording and demoing.
When in doubt, refer to Chris's post above, last sentence....