Next time you have a problem getting a tire to seat, take a tie down or packing strap and wrap it around the circumference of the tire. (I really like the BMW crate straps for this. Some dealers sell them, others will give them away)
 Cinch it as tight as you can, but make sure you can release the buckle as the tire inflates. I usually place the buckle near the valve stem, with one hand on the buckle release, and the other on the tire chuck.
 It helps to take the core out of the valve stem because it impedes airflow. Also, make sure you have tire lube around the bead area on both sides.
 The strap will force the beads on the tire outward against the rim so when you air it up the air will actually stay in the tire, as opposed to escaping from between the bead and the rim.
 Be ready to release the strap as soon as the tire starts to inflate.
Wait for the two pops, let it deflate, install the core and air up to spec.

Have you tried the "starter fluid" technique yet??!

I once had a tire blow up on me after the customer managed to break the bead wires and "forgot" to tell me.
He brought the rim in with the tire already mounted and asked me to inflate it.
The tire blew off the rim and pieces of inner tube hit me in the chest and face.

So no, I have not willingly exposed myself to another potentially explosive situation, such as lighter fluid or anything else flammable inside a tire.

My thoughts exactly, although I must confess, I find the various footage on-line somewhat amusing!!

Butane gas from a camp stove works well and wont leave any fluid to keep burning and burns at a low temp but with a high expansion so there is plenty of force to get the bead out far enough to inflate it. I have seen it done with a tyre for a 4x4 and the force was very little more than a blast of compressed air from a big compressor.

What you need to do is calculate how much gas is needed. I litre of liquid butane will give 240 litres of gas and will give a good explosion at 14 to 1 mix. A butane cicarette lighter would supply enough gas to seat 3-4 beads on a large motorcycle tyre.
1 litre of liquid gas would seat the tyre on a coal mine haul truck.