One amp per .001" =63 amps. Puddle on the thicker piece, get some filler in there and just wash the puddle over to the thin stuff and let it just kiss the thin part. Be ready to poke your filler into the thin part if it starts to blow away.
Also, I have had a lot of luck TIG brazing with silicon bronze on small ornamental pieces. It is more forgiving on very thin, non critical parts. Just keep the arc on the bronze and lead it around. The puddle transfers the heat to the base metal, the arc will blow right through. Be patient, let it cool of it gets away from ya.
Heres a couple of Jodys vids that I think might help.
Hope this helps.