I honestly enjoyed the mattress as much as my bed at home. It's this one off Amazon https://www.amazon.com/dp/B01INZBCJG/ref=cm_sw_r_cp_api_JSGUzb0GYEEBC
Just had to open it up and let it air out a day or two to fully expand and you're good to go.
Folds up great when not in use
It fits over the wheel wheels! And you're right, the storage "box" is slightly above the height of the folded down back seats. There's metal brackets on the leafs and it all just fits enough that it's snug and doesn't move around when set up.
I have a sketch with some measurements written on it that I'll dig up for you. Mattress I got from Amazon, wood is just 3/4th inch Furniture wood from Home Depot.
Works great, I've driven a 500 miles with it permanently in the back and haven't had any problem with movement or shifting. Also is a good way to organize the trunk.
Best Choice Products 4in Portable... https://www.amazon.com/dp/B01INZBCJG?ref=ppx_pop_mob_ap_share
I got you friendo. Best Choice Products 4in Thick Folding Portable Full Mattress Topper w/Bonus Carry Case, High-Density Foam, Washable Cover - Gray https://www.amazon.com/dp/B01INZBCJG/ref=cm_sw_r_cp_api_i_a9BGFbGVS7HDW
There is a Metolius crash-pad in some of the pics, also a tri-fold mattress.
I don't think this was the exact mattress I bought, but very similar to this: https://www.amazon.com/Best-Choice-Products-Portable-High-Density/dp/B01INZBCJG/ref=sr_1_7?dchild=1&keywords=trifold+mattress&qid=1597881037&sr=8-7
I got it off of Amazon, it’s the same one that this guy used in his build which inspired mine.