It was dark and drizzly when I just decided to put the valve stem back in and put the latching chuck back on (although later I found a neat trick that I will try with the next tire).
It turns out that having the valve stem in or out really made no difference whatsoever, it seems, with respect to getting the air inside and getting the bead to seat.
The trick to seating the bead is really to have two hands free to hold the tire edges and jiggle, wiggle, coerce, tug and jerk the tire as it's loose when you're trying to get the bead to seat.
Once you get the tire in a certain position, you can just feel it starting to blow up, where it seats and finally pops a few times as you work up the pressure to 40, 50, and 60 psi.