On a thick band , I would start w/ a seam that meets in the cross
sectional center but not at the edges, sort of like this: )(. This
allows you to fuse(weld) the interior on out w/ out frying the
exterior. It also gives you a through and through weld. To fill in
the outside, either place the ring in large tweezers and squeeze as
you melt, or simply add some of the same metal as a filler as you go.
Either wedge a small thin sheet into the seam, or add material as you
go as small chips. Remember that since you are fusing, you can add
extra material, as long as it’s identical to the original. Also, if
you can, it’s a good idea to forge the welded area to reduce the grain
size and “densify” the weld.
Good luck, Andy Cooperman