Well, I bought tubes today at a decent price ($10 ea).
But then I discovered the valve stem hole on the wheel isn't quite in the right spot for the tubes!
AND THEN I discovered that someone has maybe already tried gooping the tires to seal them: there was a not small amount of greasy snotslime inside it when I got the bead off the wheel.
So I'm taking a chance on the valve/hole misalignment. I put the inner tube in with the somewhat off-kilter valve angle and aired it up. As long as there's adequate pressure (no movement of the stem against the edge of the valve hole), it shouldn't chafe through.
Also, the wheel wouldn't come off the axle (rusted together), so I had to do all this on the machine. Fun fun.
I might have bought those airless wheels if I'd known about them first!
It's almost like we're living in the future.