I have what I believe to be a problem similar to yours when profiling an amp with either A) a lot of high end (bright switch on) or B) TONS of gain (5150 III Stealth.)
I have a Matchless Chieftain that has a "Brilliance" control that adds high end that is far higher than most of my other amps (I have a lot of amps
If the amp is totally clean, the Brilliance control won't really be an issue, but if there is any gain at all, and the Brilliance control is one, forget it. The original profile will be 90%... refining immediately goes from bad to worse. So I just EQ and adjust other settings without refining on those, and they aren't quite as good.
A friend of mine brought over his Honey Bee amp. Again, with the bright switch on, no dice. Turn that bright switch off, no problem at all. That amp is an "SRV" level of gain, so some overdrive, but not a ton... similar to the Chieftain.
I also had this issue occasionally with my 5150IIIS 6L6 back in the day. I would have to use an EQ pedal to reduce the gain to get it to profile, then add the gain back in later. The EQ pedal worked because it still allowed the gain pot to be in the same place, thus keeping the tone consistent, even though the gain was lower. That actually worked pretty well.