Both tires mounted.
I couldn't find a ratchet strap, Scottie, so I filed that idea away for future reference.
Malky, it was your idea that was the most helpful, I think... pull the valve stem core and blast air in. The tire inflates quickly, just a handful of seconds, and deflates almost as quickly! The tire sidewall-stamped maximum pressure is 42psi, so I set my compressor regulator to about 40 lbs for starters.
I've heard that Windex (glass cleaner) was an effective lubricant that dries quickly; that's what I have on hand, so that's what I used. What I ended up doing was laying the wheel on its side (on top of the old tire to keep the rim and brake parts off the floor), and applying Windex to the "trouble" spot that wasn't popping into place. Then I pushed in and unseated the tire across the rim from the trouble spot and knelt on it to hold it down in the center rim depression, in hopes that the trouble spot would rise and pop into place. At first, the seat I was holding down with my knees rose back into place, lifting me with it, so I removed the air hose (the tire quickly deflated again) and repeated the procedure, exercising the trouble spot and making sure it remained well lubricated. As I repeated the procedure, between slightly adjusting my weight on the tire, and, I believe, the residual Windex under my knees drying to diminished effectiveness, eventually the bead popped evenly into place. Flip the wheel and repeat. Took a little time, but it's done now!
As I said before... I could easily have changed those K70 tires on the side of the road... not these babies!
Thanks again, guys!