Nick- When you redraw after annealing it gets work hardened again.
When I solder things that have been work hardened I anneal very
slowly with a large softish flame starting at the apex of the bend
opposite of the seam. I slowly heat and watch it open up. As I
continue to heat around the rest of it, it should relax and go back
to being closed. I rarely have a problem with it. Sometimes I just
need to hand burnish the seam a little to snug it up.
You may want to try wrapping with binding wire, anneal, remove the
binding wire and then fuse rather than solder if you can.
I love making tubing just to my specs. It’s a good skill building
exercise, you get exactly the tubing you want and it’s cheaper than
buying it too.
Have fun and make lots of jewelry.