Hi Shawn. I'll take a stab at this...
Yes, he could. It would require turning a blank out of an applicable tool steel while leaving a certain amount of material on the ID for polishing, having the blank hardened, then cutting/polishing the working surfaces out after hardening while maintaining the finished target dimensions.
Yes. I'm thinking the ID of the die would need to be in three sections: a throat (for guiding the .375 bullet in straight), a leade or draw (a tapered section for gently decreasing the OD of the bullet down) and a barrel (straight section that actually sizes the OD of the bullet). About the same as the cross section of a rifle barrel forward of the chamber.
This would be the part that would need to be played with (by me, at least. I'm not an ME). I would
guess springback to be in the .0005" to .001" range, depending on the alloy of the jacket, hardness of the lead core and the type of lubrication used during sizing.
I would think something in the .5*/side range should work. With the .009" difference in bullet sizes that you list, this should come out to just over 1/2" of leade length.
The entire die could be made at roughly 1.25" long, and I would make it at least 1" diameter if I were doing it (standard stock size). It'll be a lot of fussy work, and will require flipping and accurately re-indicating the die to cut it from both sides along the same centerline. Also, you'll need some very good gauging for manufacturing this.
Myself, I'd just buy .366" bullets, but that's just me. Good luck