Brian,
I think that sections of foam can be cut and stored in the back portion (section by the wall) of the bed or an inflatable mattress can be used which takes virtually no storage space.
I never made the bed-in-a-box since I found an old camping cot frame to which I added removal slats and place my air mattress when I visit Dad. My last visit got nixed because of the present fiasco. Because of winter travel I haven’t visited since last fall and at 102, I’m not certain if there will be another time.
L/W
“Those who would give up essential Liberty, to purchase a little temporary Safety, deserve neither Liberty nor Safety.” Benjamin Franklin