My vacuum(s) cannot be pushed on my newly installed carpet
Try going at it from a different direction. I have a low-pile rug that refuses to be vacuumed from one direction. Even while it's off, you can't push it that way. 

Also, try pulling and never pushing; tip it up to advance, then let it touch down and pull backwards. Again, one direction is probably easier than the other.

If it wasn't stretched well, you'd probably be bunching it up just walking on it, so I think you'd know. Stomp your way towards a wall, if it bunches up, it's not stretched right.