I'm sure you know to push the beads that are already on the rim to the trough in the center of the rim and finish near the stem. If you finish opposite the stem, the stem prevents the beads from going down into the trough.

I always start the process with enough air in the tube so it's not collapsed but usually have to let it virtually all out at the end to allow the beads to go to and stay in trough.

The hardest tires to install I've ever dealt with were Specialized Armadillos. That was 5 or 6 years ago and I don't know if they're the same now.