To get a tubeless tire to seat you need to get the beads tight against the rim so the air can finish seating and seal the tire. Then the air pressure can inflate the tire. Put a tourniquet around the tire tread and use a stick or screwdriver to tighten it. This will make force the tire beads against the rim so the air will work for you instead of just leak out. Using a bit of dish soap on the beads will help it to seal initially and lube the tire so it will pop into place at a lower air pressure.

Good idea! We were thinking of just taking the wheelbarrow to a gas station where, hopefully, the high pressure would be enough to get the wheel back on. But that sounds like a trick that's a lot more fun!

Heating the beads to the tire makes seating it easier. A well-known trick is to spray on some WD-40 or starter fluid and light it.

But the least dangerous way indeed is to use a sufficiently big air compressor and some lubrication.

Don't suggest fun tricks with fire! Mark might get excited. (At least there's no dynamite involved....)

Now you're giving me bad ideas!

I'm thinking a piece of detonation cord wound around the rim might be the fastest way to inflate a tire. Of course there's a delicate balance between inflating the tire and blowing it up or destroying the rim. That would make a fascinating experiment.

We definitely won't be trying that.