I have my big dogs upstairs often, due to claws I'm never going to touch an inflatable mattress in the ACCC. I haven't tried a Hest, I'm sure it's quite comfortable. Having spent too many rough nights backpacking with hard-to-fix holes in ultralight inflatable pads, not interested in more. YMMV.
I will caution in the strongest possible terms, never to use memory foam in any situation that might see real cold. Memory foam freezes and turns to concrete below freezing temps, and it will absolutely suck out your will to live. Getting in at first is awful, then over time you kind of melt a hole into it and sink in. Until you want to roll over, and it's a wall of ice cold concrete all around you, and the hole is shaped wrong.... I'm sure there are ways to mitigate this with diesel heat (or just avoid winter entirely lol), in which case one might never find this out the hard way
My Alu-Cab, if you close the top and slide a ruler up to measure from the base of the bed platform to the padded roof interior, I measure 7". Stock mattress is 3" and not IMHO comfortable. Do note, that 7" headroom doesn't account for things you might leave in the pockets, or the LED light which will compress a spot in thick bedding.
We use the stock 3" mattress, an extra 1" foam on top of that, fitted sheet, top sheet, and usually leave two down sleeping bags spread out upstairs. Plenty of headroom still with that much bedding, and it closes with little compression. Pillows don't fit, they get moved downstairs.
My Alu-Cab mattress measures out 81" x 48" x 3". The bed platform itself measures 82" x 52".