This would be a tough to repair the channel with the torch. Tanzanite does not handle heat. And it is not a very tough stone as far as setting. Any contact with a metal tool and it will chip the surface.
I protected the stone with watch makers putty to absorb any stray laser beam or reflection and repaired the channel with the stone in place. I built up the missing channel by slowly melting 30 gauge gold wire with repeated laser shots. Probably did about 300 hits. The ring really looked good after burnishing the shank and sanding and polished the ring.