If those are vertical compartments, depending on how thick the plastic is, you could drill in from the outside and use wire to make a hinge so they would swing open to show off the detail. I agree, would be a shame to hide all that nice work.
Might be able to do the same with the outer doors on the compartments as well, at least the ones that don't have roll up doors.
Hat off for the nice job so far, will be watching the rest of your build.