UPDATE
Wayne came down to my house, borrowed tool in hand. Unlike the horrible one I was given, this one looks like it might actually work. We eagerly set to work. After a little more than an hour of hammering, spraying WD40, more hammering, more WD40, lifting the nose off the ground, more hammering, more WD40, dropping the nose back down, more hammering, more WD40, more hammering...
... we managed to remove one and a half of the wheels.
We managed to remove the left rear and its adapter, so we bolted on one of the Camaro wheels. The left front wheel did finally release its wheel nut, but a few of the lug nuts are putting up a fight so the adapter is still in place. We put the stupid wheel back on the car just so it can rest on its tires rather than sit on a floor jack (or jack stands) for a few days.
I'll make another effort in a couple days. In the mean time, I'll be buying a can of PB Blaster to see if I can loosen things up a bit.