And I thought I was bad for miniscule issues

I'm glad you provided some more detail. Definitely a finite element analysis nightmare.... lets see .001 here, .001 there .....did one cancel the other...who really knows.....wait what about the gravity as the barrel really gets hot....with the lack of a uniform taper…..then heck what about the changing dynamics as we expose the steel to these temperature gradients. Distortion might better phrase this. Don't forget porosity and irregular chemical composition.......
heck what about an eccentric case cavity (or offset/misaligned chamber) and the tendency to apply hot expanding gases off the bore center...this might heat one side of the barrel more then the other. My goodness old low quality brass like Rem.. Win. might make this a real varying problem. Perhaps the deposits of "dirty" powder, which may accumulate on the bottom of the bore......this, may insulate the barrel or retain heat.....my goodness....
With all this warping and distortion….what about the poor relatively inelastic bullet….spinning frantically in the barrel. Then, then the poorly lapped barrel….worth 0.0001 to 0.005” of varying bore diameter….heavens what are we doing….
With quality BR barrels, particularly heavier profiles these imperfections have less affect if any detectable.
As for exposed barrels, no doubt uniforming the convection coefficient has a plus but again, in most instances I doubt it is a dominating issue, again particularly with heavier barrel profiles. It’s really a toss up. In your case you are willing to sacrifice stock stiffness, create a signature look all for uniform cooling.
Cropping the forend (height or depth) of a stock from a structural prospective should be done as a gradual taper to be most efficient in retaining a balance in weight and structural rigidity.