In my experience every amp requires different timing for when to end the refining process. My 5153 for instance profiled accurately with just 7 seconds of refining, any longer and say hello to the dreaded bloated low end, any shorter and the lows haven't filled out yet. My 6505 required around 15 seconds, my custom JCM 800 just over 20 seconds.
This might be an unnecessary or even wrong approach with the likes of a Fender Twin but with high gain amps pumping out a chunky low end through an oversized Mesa cab it is essential to time it just right. I also palm mute only as playing a variety of chords seems to keep the Kemper guessing, I feed it consistent palm mutes only and listen for the moment the Kemper latches on and nails it.
These methods for me, result in 99% perfect profiles when playing solo and 100% indistinguishable from the real amps in a mix.