With the installation of the diffusers, the lamp is now complete. 

For diffusion, I opted for Optix LED Satin HDF which has a matte side and a textured side. I thought the textured side adds a nice bit of detail and with 92% light transmission, I wasn't really losing anything. Usually diffusers that offer the kind of scattering this provides ends up with light loss of upwards of 60%, so this was a great find.

The material was only available in 2mm thickness, so I ended up slotting them into the grooves instead of giving them a lip and having them sit flush with the bottom of the wood.

Because I don't really have a full workshop set up yet, I ended up mitering the corners using a 45° rule and scoring+snapping. It worked well enough, but some of the angles didn't come out perfect and I had to hand file them to fix things up. 

I didn't miter the diffusers on the top lights to keep things simpler. I don't think there's any loss of quality with the small holes there. The only downside is that this may be a place dust can get into the lamp over time.

Over all, I'm very pleased with this project. I could have done some of the woodworking better, but considering I don't yet have a shop set up and this was my first project, I feel like it's a net success.