We could spend endless hours trying to narrow this down to something by trial and error. But at least in my case, I cannot easily investigate the effect of pick (and playing style/touch for that matter), string gauge/brand/material, guitar (and its construction/electronics), pickups, cables, audio interface, Kemper settings, firmware versions, Kemper hardware etc ... just because I don't have any extra stuff or extra time!
So unless we collect a lot of data from many users in a systematic way, I'm afraid such a reverse engineering approach might not lead to a solid conclusion.
My workaround so far is to adjust "pick", "compressor" and/or rig volume to prevent the peaks from clipping (yes, they are there but not clipping anymore).
IMO, it would be best to have the mothership comment on this in a serious manner...