I've worked in dozens of plants in numerous companies, most of which had warehouses that stored objects on shelves from 100 to 1,200 lbs. None had movable shelves. That's what pallets and forklifts are for. Objects are picked up and moved, not slid out. Shelves are for small things.
For that reason I'm skeptical anyone has designed shelves for this purpose other than in special situations, like morgues. (However, this tank would hold at least 5 times the weight a morgue shelf might be rated for.)
Having said that, the only plausible way to do it imo is using a pallet set on tracks (like the way coal used to be brought out of a mine.) A wheeled pallet would in theory work, but without pre-set tracks, it would be almost impossible to move it back in place exactly where you wanted. The tank would not be usable to steer as any pressure on the top and sides (especially if it's partly filled) would cause fractures or stress the seals.
You could attach handles and use the pallet to push and pull (the tank as it sits on it) while the track would reduce the friction and keep it aligned. That's basically how movable shelves (and drawers) work. Would probably need an industrial grade pallet and wheels.
In short, the bottom of the structure would simply be an empty space where the tank would fit. No tipping concern since it's not connected to the stationary structure (above,)
Anyway, that's my 2 cents.