If you are already good at TIG and need more than 30 minutes to figure out how to braze a joint you better pack up and go home...

Harris 50n or 56n with Staysilv white flux works very well for stainless steel brazing, most welding supply shops have the 56n. The 56n is very easy to use. The 50n is easier to make filets with but you usually have to order it or buy it online.

BTW after you make a cage you will see why they cost so much, They are a PITA to make