John in NM
I think you'll have trouble with re-heat treating after either brazing or silver brazing. Either process will draw far too much temper but not get hot enough to re-temper. Less of a problem with a HSS bit I bet, just like with carbide.

I think your tig welding idea has merit. Hard part is keeping it flat, but I from the little welding I've done I think it may be possible for a patient hand to do. Trick is to keep the welds as small spot tacks, flipping frequently to keep the pull even. Overlap tack upon tack until you have the V filled on both sides, then re-harden the piece and hope nothing moves.

High Carbon rod would be best if available. That's where a lot of my inexperience shows - I've only done this kind of thing with mild steel.