Yeah it's so frustating I have a brand new (6 hours) Doosan 3K cushion tire LP forklift where the cage will go under but it's triple stage mast is about 2 inches too tall. If only the dumbass home garage door builders would make 7 foot doors actually 7 feet tall. In this case it's not just the doors that are the problem but an overhang in front of the doors that is 81 inch clearance and would be a major project to change.
Not everyone is aware thay ain't the same critter, but the US Army CONEX of the 1950's and '60's - coupla hundred thousand used Korean & Vietnam wars - were only 6 foot ten inches high vs today's intermodal containers of 8 foot six inches.
The FL of matching capability included the Towmoter 4,000, short mast. Mast was triple, not double, cage low-height as well.
AFAIK, triple stage outright dominates in "really short mast" FL- many of them meant for work inside railcars, trucks, and CONEX container applications, but not-only.
Those could drive right inside a sub seven-foot CONEX container, still get a pallet off the deck, then put the load up around 10 or 12 feet once back outside. 4K was a VERY conservative rating as well.
Cannot imagine no one still making comparable capability - but perhaps not in all that much lifting capacity.
Limiting factor MAY have been what the floor of the CONEX could stand from the point-contact load of the tires. Even that 4K Towmoter had duals at the mast, twinned third-point rear, pneumatic, all around, and not all that small in diameter, IIRC.
2CW
...and the curse of a 76" garage door here to a mere 8-foot ceiling, anyway, so .. two toe-jacks added to the arsenal since last we met, and skates? Hah!
Lots of skates, Vestil "economical", & Northern Tool "El cheapo" - both more than good enough for my modest duty-cycles.
Chains, ropes, straps, and long timber pusher/puller bars then let me work fully 20 feet back into the garage/shop with rented FL still outside the door.
Bit of a PITA, but it works well-enough.