Get someone to help you keep the opposite side of the tire into the recessed area of the rim.
I'm thinking that would definitely help.
Trying to remember a trick I used. Ratchet straps I think it was. Around the tire tread and bead, to pinch the beads together.
I was thinking something like that might help, just not sure how you would get your strap out once the tire seats.
Before I take the wheel and tire to a shop I'm going to try 3 things:
1. leave the tire in the sun for a few hours and try it when it's hot
2. Built a square spacer box out of 2x4 to keep the brake disc off the ground so I can try this on the ground. My wheel holder is actually pushing the tire up from the bottom, making it more difficult to get the beads into the recessed area of the rim.
3. Once on the ground use either a 250 lb friend to stand on the tire on the opposite end to compress it into the recessed area or try to use ratcheting straps to compress the beads together.
Again, unless you have held a 180/55/B18 D407 in your hands you cannot appreciate how stiff it is. At least 2 times stiffer than equal sized radial tires. I layed it on it's side on the pavement and jumped on it with my 150 lbs and the beads only compressed about 1"!