I thought you saw mine when you were here. I keep all mine on the top shelf of a rolling cabinet. The top has an oiled wooden surface.
I used to keep them on the top surface of a tool cabinet. But that required a lift to transfer.
A back is a very precious thing. Mine isn't in great shape but it's way better than many my age. I'd like to keep it that way. Lifting heavy objects from down low is a bad idea.
By putting such things on the top shelf of a rolling cart, I can roll the cart over to the mill and simply slide the heavy tool over onto the table, and slide it back when I am done. I can even raise or lower the table so the transfer is always a downward transfer.
I've also considered a small gib crane, but I think sliding is even easier than attaching a crane.
I plan to replace the wheels on my cart with bigger easy roll ones in the near future (famous last words).
The cart can be stored anyplace it can be rolled to, but nearby is convenient.