I am always looking for a better rock solo sound (with most of my gigs, it only gets used once, maybe twice a night, so I want it to be awesome ).
I spend a ridiculous amount of time auditioning profiles looking for a better one and that is my suggestion to you: keep looking for the profile(s) that are the closest to what you are looking for. I keep a folder in rig manager that I put any potential solo profiles into. I also keep a couple of performances with potential solo profiles, just so I have access to them when I don't have rig manager with me. My current fav is Bogner Ecstasy Ch2 N2 from a certain "Lone", "Amazed-ing" profile maker .
In addition to the all the great suggestions the other posters have made, try these:
I have noted that some really distorted profiles smooth out and fatten up when the gain is lowered, while still having plenty of sustain. (This also works great when looking for clean/cleanish tones.)
Take which ever profile you are considering and crank both the Middle and Treble knobs on the front panel to taste. I really like this, but I am aware that some of what I am liking is Fletcher-Munson related. Depending on how much you raise them, you may have to lower the rig volume to compensate.
Caveat to the next suggestion: I hated chorus on distorted guitar tones in the 80's and I still hate it (apologies to Zakk Wylde). Judicious use of some kind of chorus/micro pitch can smooth things out. With the Kemper's ability to mix the effects you can get that smoothing effect without the "chorus" being obvious. Try the Air Chorus or the Micro Pitch.
This next one is counter-intuitive: I find that if I lower the volume and/or the tone knobs on the guitar just slightly, some tones smooth and fatten. See if that works with your rig.
Lastly, an observation: I find that when I get a really fat, smooth solo tone that I like, it is often unusable for rhythm/chords. I assume it's just too gainy, too fat, etc.
So, just my thoughts, and I am searching right along with ya!