We added the lid on top of the enclosure. More work is needed to complete the box.
We made the closing lids by cutting a 1/8" acrylic panel. A strip of soft foam was added between the frame and the lids to form a seal.
We did a qualitative test by placing a white noise source inside the box and listening. The aluminum bubble wrap we used did not provide good noise reduction. So we replaced one side by a plastic piece (~1/8" thick) with a damping pad on. It could damp the noise pretty well. I'll borrow a blue bird microphone from Den tomorrow, so we can measure the TF or just the relative noise signal to check how much attenuation we get from our structure.