I suggest you check the bottom unit of your mattress set, and see if it really is a "box springs" unit, or just a foundation unit. I have noticed that in many newer mattress sets, the bottom part is just a framework with a solid top such as plywood. If this is the case with your mattress set, you could add a plywood top to your framework, and place the mattress directly on the bed without the lower foundation unit. This should lower the top of your mattress to a more normal "bed height" while still providing lots of storage area.
Just be sure that your framework is solid and that the top of the plywood is nice and smooth. On the unit I built (a murphy bed) I went so far as putting heavy cloth on the top of the plywood so that the mattress wouldn't be directly on the wood.
Keep in mind that if your mattress set is new, that using the mattress without the matching foundation unit will void the warranty, even if the bed and framework you build provides better support than the factory unit.
Just be sure that your framework is solid and that the top of the plywood is nice and smooth. On the unit I built (a murphy bed) I went so far as putting heavy cloth on the top of the plywood so that the mattress wouldn't be directly on the wood.
Keep in mind that if your mattress set is new, that using the mattress without the matching foundation unit will void the warranty, even if the bed and framework you build provides better support than the factory unit.