I never thought of that liquid solder! I'll have to see if my hardware store carries it.
I also do the steel wool cleaning trick you mentioned, after reading it (maybe from you!), to remove the old solder which leaves a clean thin white shiny area to solder against. Really works!
Sometimes when rigging a joint, I cut a length of solder and place it along the seam with tinning solder flux as stickiness to keep everything in place (along with gravity) basically what Wilesco does with inserts.