I think the biggest problem with the cubby is that bottle jacks don’t like being stored on their sides. Even the ones we have at work for rescue applications, manufacturers recommend that we keep them upright. Experience seems to show that bottle jacks are as inconsistent as it gets. Those that have been stored on the sides crap out. Upright craps out. Just like guys have bought cheapos that last forever and higher end bottle jacks crapped out. I had a tractor supply jack that fell over in the back of my Jeep and didn’t work when I needed it. Got one from Lowe’s that came in a case and is strapped in upright and is still going strong 5 years later.
I think the only good answer to a bottle jack is if you get lucky or not.
As for size, a 2 ton will work for a tire change, but you’d have to let the air out of a tire and test fit some cribbing to see if it will lift you enough to get the other tire on. All of us have different tire sizes, so what works for some, may not work for you. I know I wouldn’t want the added headache of letting the air out of my spare to get it on and then have to air it up. So I run with a 6 ton and a plate which is 10”X10” 3/4” plywood, 3 layers glued and screwed with a set of 2X4 wedges to snug it in. Gives me enough space to get a fresh tire on.