I've moved 55-90 gallon tanks across rooms before without a full drain.
I took about 80% out, picked up one end and slid in an upside down rug/welcome mat (so the rubbery bottom was up but the fluffy part was face down), picked up the other end and did the same, then dragged it across the room, clearing out space to set up the new larger tank. I did the same with a 90, just rotating it 90 degrees and sliding it about 5 feet, though that one was much more difficult.
I of course have hardwood floors and am a competitive strongman, so I guess that made it a bit easier. Still, under the right circumstances, it can be done safely. The key was the little rugs underneath. No way it happens without that. I have dragged my 50% full 110 out a few inches before to check for leak damage, but it was almost impossible to put back into place. Took everything I had.