I had this problem with conti GP 4000's, they just wouldn't go on the rim.
The last part that you're stuck on, I just point it downwards towards the floor, supported on either foot. Then I grab the tire and try and squeeze with both hands outwards and towards the part of the tire I can't set on the rim making sure the bead is as close to the center of the rim as I can. It won't feel like you're doing much, but that's usually enough to stick a Pedro's tire lever underneath and ease the rest of the bead into the rim.
Hope that helps.