The last bit is easier if you press the opposite end of the bead you're working on--the other side of the whole wheel from where you're working--to the center and let it drop into the groove track in the middle of the rim--that will give more slack on the side you're working on.
Re your specific issue, use two irons, one on each side of the problem. One will hold the tire tire on the rim where it belongs while you use the other to get the other end over the hump.
Last edited by mdarnton; 09-24-22 at 03:57 PM.