Thanks for all the great advice. I will give some of the local tire places a few calls and see what develops!
I especially appreciate the advice on bias ply vs. radials. "100% period correct restoration" is definitely not what I'm going for, though I admit I do like the way those old tires look. I'm going for more of a "stock looking driver with some safety updates" approach.
In other news, I got my primered rear bumper on today, with the license plate bracket, and it looks pretty nice. The bumper isn't totally straight, but (see above) it's fine by me!