That’s what I would do. Get a scrap frame from the dump/wherever, cut one or two bits of tube for patching. You will probably have to open out the tube a bit to fit over the existing frame tube. I use silver solder because it’s easier to get the work up to temperature for the spelter to flow.
There’s a thread in technical too good to lose about “ going to try brazing” or thereabouts.
E bay is a good source for small quantities of silver solder and flux….. look for “Johnson Matthey “ branded solder.