Couple of thoughts on inflating difficult tires.
If you can get the tire warm, it is much easier, yes, the wife got pissed when she realized the "cookies" I was baking were round and made of rubber.....
If you do a particular size of tire a lot it is worth making a ring, or buying a tube that will fit the gap, not to install in the tire, but to use as a tool. On the specialty off road motorcycles I ride (observed trials) we have tubeless rear tires that can be a real challenge. We now have large rubber foam type O-rings, what you do is seat the bead on one side of the wheel, then push this well lubricated O-ring into the gap on the other side and inflate, it will push the O-ring out as the tire inflates. The same can be done with something like a bicycle inner tube to fill the gap, lube it well and pull it along out of the gap as the tire expands and seats.
I also use a tiger tank on occasion, basicly an air tank with a dump valve and it blows the air in through the gap in the bead, the sudden inrush of air generally seats the bead.
One thing that many folks do not do, that is really the simplest to me is first, get the tire and rim suspended, so you can manuever the tire around on the rim and help to get it to bite in. Remove the valve core, this allows more air to enter without the obstruction of the valve core, and use a high volume / pressure blow gun to do the initial inflation of the tire. I am able to reset many tires just using this techniqe.
Another thought is when you purchase new tires, and the beads are pinched together, wedge some appropriate spacers in place between the beads and spread them apart and allow the tire to stand that way, remove them just prior to installation, Beer cans work excellent in a 4.00 X 18 trials bike tire....