I also spent a short time in the shed today attempting to put a supposedly Welsh Willy Supersport tuning kit into my Supersport but unfortunately it's way too big for mine and the spring won't even go into the piston, anyway that will be sorted soon with the help of Tinners.
I've found the easiest way to get the barrel back on to any of the BSA break barrel range is to assemble the plunger/spring into the breech block with it in the right position for the bolt to go through and then push the breech/barrel into the cylinder jaws lined up as if it was in the closed position and then when it is in as far as you can get it, you will have a small gap were the plunger is up against the cross pin, all you have to do is then push the end of the barrel down firmly (making sure the cylinder is against the floor) and it will slot home, you can then push the breech bolt (or pin like on most models) in and you're then sorted, I used to struggle trying to push the plunger down against a bit of wood and get the pin in at the same time but trying to balance the whole cylinder/barrel set up wasn't easy.
Another little thing to look out for is to check to see if the bolt that holds the back block threaded cup to the trigger block (Chambers numbers B1313(nut/bolt) and N116(threaded cup)) is tight when you strip the rifle for inspection/service as it can come loose and will make the back block spin and not undo, this happened to me once on my Challenger and I had to cut the back block off and chisel the threaded cup round to get it out the cylinder and buy a new back block, you will need a very thin walled socket to do the bolt/nut up with.
Hope my way helps.
Pete