Mark, we may have to send you to the countryside for re-education (which you may be too young to recall was the treatment for cultural revolution Chinese who, um, needed re-education.) Tweaking or adjusting or perfecting a gum print is just that. It's how a gum print is made. It's NOT power saw and belt sander, charming as those tools may be.
Once I had photoshop & an inkjet dialog that offered a curve, I "curved" a gum neg simply by shortening it to the number of steps the emulsion would print -- or maybe one more to allow for development strategies.... To have a SPECIFIC curve beyond that would put the gum printer in a box -- having to make one particular kind of print -- at best. What you call "saw" & "sander" (or maybe that was "hose"?) are how you make a print, so you offer to eliminate the basic "tools" of gum.
I also suspect that Katharine is right -- that every change of pigment, and mix, every new batch of sensitizer (they tend to lose speed as they age), every new purchase of gum (which changes drastically from maker to maker, and also season to season) every new tube of paint (they've been known to perform differently, even when officially the same) AND every MIXED color (which would surely change the "curve") would require a new curved negative. AND if you decide to avoid such changes as far as possible to keep your nicely curved negs viable, you will be, as far as gum printing is concerned, tying one hand plus 3 fingers behind your back.
I used to teach gum as the 2nd process, after cyanotype, but before VDB, that is, to get students used to mixing, coating & using a large negative before letting them loose on gum -- (platinum was the 2nd semester) -- but now I'd suggest in these times, maybe it should be first, before the brain washing sets in...
(Watch for comment from Demachy to follow)...