A framebuilder could do this in a sound way. The best approach is to do as much as possible cold, i.e. cut off the bulk of the posts and work the area back down to smooth with files and then sanding.
For the most part, it sounds like a giant hassle that accomplishes little and is founded on the misconception that cantis aren't good brakes.
One exception to that could be if there's something about the frame/fork design that made cantis a bad choice. For example, if overly flexy stays or blades were used, performance with cantis can be lacking. If this is the problem you're trying to address and you're willing to go to this length to do it, going to direct mount centerpulls like Mafac, Herse, or Paul would be far superior to a caliper in terms of braking power, assuming this bike has the kind of clearances that usually go along with cantilevers in the first place.
You haven't mentioned reach measurements, but in the more normal case that this is some kind of typical hybrid/touring/cx bike, it would probably need very long reach calipers to use the existing bridge and fork, although the bridge could in theory be moved. Those kinds of calipers are pretty mediocre brakes compared to a well set up cantilever. You'd be giving up a lot of function.
If you want the bike set up to not have any use for long reach, and again assuming it's a clearance-heavy bike now, then probably the best path would be replace the fork entirely rather than rework it, and move the bridge. That way you can use any reach-appropriate off the shelf modern caliper with a recessed nut front and rear without having to screw around with either adapting modern brakes to non-recessed nuts or working with the few extant options for stock non-recessed nut calipers.
I wonder if you're using basic smooth post low profile cantis and making the assumption that other types are equally hard to live with, or if the bike is set up to create excess shutter off the front brake. These problems are all solvable with less extreme measures and certainly with better results than an ultra long reach caliper.
