It regards to joining a double rifle a (High force?) solder is used to perform this task, admittedly this will be difficult to solder inside a barrel; but with an extremely hot piece of iron made to deliver the heat to correct area you should be able to then fill the void (after cleaning & prepping) like the old separate heat sourced soldering irons.
To redo the chamber after a small dab is put on again will be a tense moment, but if set up right & taken very slow with a finishing reamer - I believe doable!
I am no metal smith, so I'm only throwing suggestions out there to far more knowledgeable folks!
To repair an old rifle back to shooting condition certainly is a big ask, but if it was say your great grandfather's & it had history & real semimetal value to you....wouldn't you try to get it going again?