The 3" bed of flourite obviously adds weight, but it also helps spread the load evenly which is a good thing. I'd remove the large rock (just to be safe in case it falls against the side glass or something), drain as much water as you are comfortable with, get 2 ppl to lift up while a 3rd places a piece of ply or MDF underneath. Set it down and and move it on the new base. From there you can reverse the process at the new location.
Just go slow and make sure there is no water on the floor or obstructions in the path (including mobile ones like kids or pets) from point A to point B and you should be fine.
When I was about eleven I took a 10 gallon terrarium outside to clean it. For some reason I decided to move it (1/3 full of water) and somewhere along the way I got tired and set it on a 6" diameter flat tree stump. DON'T do that!