^ All this, plus...

And after finally getting the last bit of bead snap-rolled on, before doing anything else, before even setting the wheel down for a rest, I go around the entire circumference of the tire, pinching in the sidewalls to make sure there is no little roll of tube protruding beyond the tire bead anywhere. I, too, find I usually had to let some air out of the "plumped" (great word!) tube in order to get the last bit of bead on, and that's typically when and where the tube gets trapped. It must be completely retracted up between the tire beads and therefore invisible all the way round. All you should be able to see is rim strip. It's most important to perform this check on the side of the tire you put on last, i.e., the same side you just finished. Someone asked me once if I spin the wheel over and check the other side, too. I had to think for a minute and then decided that No I don't. But my usual drill is to put one bead on, then insert the tube, then have at the second bead.

If I find even a sliver of tube visible, I first try to jostle and jiggle it back under the tire bead. This rarely works, because the bead is trapping the tube. So the next step is to carefully elevate the tire bead with two tire levers, one on either side of the visible tube portion, but not touching the tube. Two tire levers that close together may not fit under the bead so one or both may need to be a small flat screwdriver. If there is any air in the tube, this may be enough to allow it to retract under the bead. If not, leave the tools hooked under the bead and ask your assistant (that's the great thing about riding a tandem -- you always have an assistant ) to pump a few slow strokes of air into the tube while you maintain pressure on the levers to keep the bead off the tube. This will do the trick. Then repeat the circumferential check. (It strikes me that it might be more efficient to re-plump the tube before doing this check, so that elevation of the bead will allow a protruding segment to snap back spontaneously....but air will make everything just a little tighter and it might be impossible to get a tool under the bead to elevate it in the first place. Dunno...)

My wife has the knack for using a tire lever to mount a tire without pinching the tube. I was much impressed when she showed it to me... and it was the inspiration for my Johnny Carson tag-line.

After partial inflation (to 15 psi or so) I wrestle with the bead as per Canklecat to make sure it is seating.