We used three 8 foot 2x4 boards and ran them under the crate (side to side) to give us 3 handles to lift from on each side. Not attached, just slid through under where the fork lift would pick the crate up. Your 6 friends can then easily lift and carry the entire crate and carry it to the door. Then switch to the suction cups. I don't think you will need the dolly doing it that way.
BTW you have 5 or 6 friends now... count on having 2 or 3 friends after the move. lol
Good luck, pics or it didn't happen.