There are advantage and disadvantages of running drawers; they surely are not the end all in economy of space, ease of use, and efficiency. On the same hand, they do provide many advantages over stuffing boxes in an enclosed sleeping platform. I've been running boxes and bags under my platform for a while and thought I always wanted drawers; now my mindset is a sliding platform that houses boxes that are accessible and I get the best of both worlds. (see build thread).
Nice work by the way on the construction of the platform and spaces. IMO, the use of drawers with no access from the top is the way to go for your application. If you were to stuff boxes under there and have a flip open top on the platform where you can access the boxes then I would say that would be your best bet; right now, your situation is kind of what I live with now; if I want to get to something, I have to pretty much pull everything out one at a time to get what I need and it suuuuuccccccccckkkkkkkkkssssss. That why I think you might like the idea of drawers instead of individual boxes.
My platform idea is a single pull that gives me access to all of the boxes. On that note, I am also installing more top access doors that allow me to get into things without having to pull the slider out or open my tailgate. The design is more work and probably costs more but its a one time deal so I buy now, cry now, and enjoy the right application for life.
Interested to see where you go with this; Nice work!