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Tossed it on the floor, threw a sheet over it, then my top sheet and comforter. The "headboard" is my wall.
I think real tatami would give a slight bit and make it less hard than my carpeted floor, but that's just a guess. Like I said, I think you could toss it on a box springs just fine.
Also just FYI Chinese mattresses are incredibly hard. They're almost impossible to find in the US but I think they're ideal. My wife and I had one as our first bed and the thing was just great, but we lived in her home country at the time.
Here's the shikibuton I got. I am sure there are better ones but I just needed a cheap sleep.
I have this one: [link]
That brand makes other sizes / colors. Honestly, I can't recommend it enough. I've had it for a year now and have slept on it every single night in that period of time. It definitely has gotten a bit "worn in" and isn't as cushy as it used to be, but it's still super comfortable.
Honestly, the only problem I've had with it is that it did have a very strong smell at first, but some fabric spray and a day of airing out worked wonders. Would also highly recommend a mattress protector.
Feel free to message me if you have any questions at all!
Speaking of which, I got a 'Japanese-style futon mattress' on amazon and it's worked great. Obviously meant to be folded in up to ~90 degrees (though with my build it doesn't get past like ~135). I'm sleeping on mine full-time so I threw a 2" memory foam topper on for extra padding and it's worked great. The only thing I'll say is that the futon might be a little more difficult to cut (if you don't fit in one of the standard sizes like I did) since it'll require some sewing, but still entirely possible. You'll have no problem with any modifications to the memory foam
Futon Mattress: [link]
Memory Foam Topper: