How did you compare the KPA with real amps? Did you stick your ear right next to the speaker like the mic that captured the profile was probably positioned? No, right?
Therein lies the problem: the KPA is supposed to sound like mic'd amp in your typical control room. I know, I know, we want the tone to sound like what we're used to get from the real amp, we'll get to that. Here's a list of things you can try in order to have profiles sounding more like the real amp:
1. Not necessarily related to mic'd amp vs amp in the room, but mind your clean sense setting - you'll find that lower settings help with the harshness and improve dynamics. Lately I've also been playing with dist sens as well, it's an interesting control that helps finding the profile's "sweet spot" for your guitar. CK says it's identical to turning down the gain control in the amp block, but 1) I prefer to preserve the original profile gain setting and 2) if you put, say, a green screamer in front of the amp, the dist sens control will affect the input of that pedal and not the amp anymore.
2. EQ. That's what engineers do when they want to get that raw guitar tone they've captured into a polished, good sounding tone. Here's a starting point for thin and harsh tones: dial a studio EQ in the "X" slot and set the 1st parametric band to Freq 160Hz, Q 0.6 and boost by 1-2 dB until you get a nice "oomph". Then adjust the high shelf to around 5.5kHz and cut by 1-2 dB. If by doing that you lose too much of the good top end, use the 2nd parametric band to add 0.5 dB around 2.9kHz with Q 0.6.
3. Reverb helps add room ambience that isn't part of the profile and won't be there (from the actual room I mean) if your monitor is pointing directly at you. Well you should add room ambience if you're recording anyway, and I personally do it live as well. Here's a starting point: small room with time 1.8s, damping 5.0, mix 40-50%, bandwidth 3.5, frequency -1.5. Then add delay to taste if you like - you might have to lower the reverb mix once you turn delay on.
4. If you're still getting some ice picking on the high strings, try raising the bias in the amp block to something between 1.5 and 3 and/or lowering the definition parameter, but not by much otherwise you'll lose the original character of the profile.
5. If that isn't enough you can also try to lower the high shift in the cab block by -0.1
Good luck!