I did my bed this way. The outer frame is made with 2x10's if I
remember correctly (can't go check because SWMBO is in the bedroom
sleeping on it). Within the box frame, I put 2x3 "joists" at roughly
12" on center. You could actually use joist hangers to attach them to
the box frame. I didn't think of that at the time, and built
essentially the same thing out of wood. Anyway, on top of all this
framework I attached pieces of 3/4" plywood extending to the exact
dimensions of the mattress, about an inch beyond the edges of the box
frame. I rounded the edges over with a router, and the mattress sits
directly on top of that. I don't use a box spring; I find the bed more
comfortable without it, and it would be WAY too high if there was a box
spring.

I designed mine so I could take it apart again to move it. All four
sides of the box frame can be separated; one has the headboard
integrated. The 2x3 cross members unscrew and pop out of their
hangers, and the plywood pieces (I have 8 of them) are individually
numbered and unscrew as well. Other than the mattress, the whole bed
can easily be moved by one person (albeit in multiple trips).

The bed went about five years without squeaking. It has recently
started doing so, and I've been too lazy to fix it. A screw has
loosened up on one of the cross members. If I didn't care about the
ability to break it down in the future, I'd use construction adhesive
on everything, and I'm sure the squeaking would go away and never come
back.

22" of height underneath is a LOT!!! Even without a box spring, you're
going to need to pole vault into bed. Can she substitute a larger
quantity of shorter Rubbermaid tubs? We store clothes, shoes, etc. in
rather flat ones (maybe 9" tall) which are short enough to slide under
the perimeter of the bed. Once underneath and beyond the thick "rim
joists" of the bed frame, they can be stacked two-high. I think we fit
12 or even 16 of them under there with no problem (it's a king sized
bed).

BTW, we just use a normal bed skirt (bed ruffle? Whatever the proper
name is) just as if there was a box spring under the mattress. You'd
never no there was a significant wooden structure under there.

Josh