There was a pretty extensive discussion last year about how much space a queen needs to lay at her potential. When you do the math based on 2000 eggs/day, it works out to 7 or 8 deep frames. Granted that's edge to edge brood frames, but still, one 10 frame deep box is enough to have a full size brood nest. Are you running a queen excluder? If so, that's probably the issue. bees like to store honey above the brood, so one possible manipulation is to reverse the deeps so that the brood is closer to the top.
My bees are not reluctant to move up. In fact they prefer to expand up rather than to the sides. For that reason I leave the supers off until the bees are occupying all the frames in both deeps. When they're like that they give a collective sigh of relief and move up into the spacious super right away.