especially as you alter the parameters in the profile away from the captured settings.
Let's say that the way the Profiler alters the parameters is consistently the same.
The Gain and the Tones in the Profiler are linear and don't interact with each other like in most amps. Gain alters... gain only, and not tone as well. A tones knob's effect doesn't depend on the other knobs position... and so forth. This is by design.
Of course what I just wrote is not strictly related to what you're discussing, but might be a way to rephrase your initial quest: the Profiler has a "same" way to alter all the profiles' sound. Which doesn't reduce their initial differences tho.