I would imagine some trauma to the bell has pushed the bell-to-body brace into the body which then caused it to come away from the two adjacent tonehole stacks causing the leaks. I think you were wise to push the body up to meet the stacks. You were intrepid with your soldering operations and could very easily have found yourself chasing your tail. A contemporary fix these days, as suiggested below, is to flow in some supa-glue into the cracks.
I don't like saxophones - can't stand the sound *but* I really enjoyed the video. Very satisfying to watch you struggle and overcome the difficulty of the repair process. Well done.
I've repaired a sax with soldered on tone holes, just flow a bit of super glue into the cracks and you will save the finish of the instrument. Because trying to soldering them back on can do more damage and you will be turning it into a nice looking lamp.
You're right about not enough heat, which is compounded by the wet terrycloth. Also, waaaaay too much Flux. Solder flows wherever flux is and you only need solder under the tone hole chimneys, posts, etc. You want to apply flux, heat it just enough to get it to wick into where you want the solder, then clean up everything else thoroughly. Then when you apply the solder, it will flow only into the space where flux remains.
You'll never be able to duplicate the original resonance of the saxophone this soldering stuff is unnecessary and I think doubtful that the solder was designed to work with this type of metal. Just use epoxy resin and epoxy resin+carbon fiber mesh. It's not going to be Mozart but it will be good enough to get a kid through a semester of band before they quit or decide to invest in a more professional instrument. Good channel though, thank you. I don't want to discourage you from doing it or even continuing to try and do this to learn from it or prove me wrong.
@@HackaweekTV Interesting. I confirmed that with my British parents! (who knew!) . ..but I think here they pronounce it the American way too. hah ;) The haven't stuck with their traditional ways I guess.