Removing plastic when growing micro-greens

Using wood and stainless steel to get the job done....  

That's great. I might try the same thing in just one tray under grow-lights.

I read a book about a couple in France who started all their seedlings for their market garden in homemade wooden boxes.

"Mike" is using cedar - we tend to think it will discourage growies, but I suspect that so long as he's changing the water regularly, and using fresh soil for each new lot of seeds, any tendency of the cedar to discourage growth seems to be minimal enough to not hurt the seeds/plants. In my climate, I'd worry about mold, and the cedar might be a good choice against that. Sun solarizing the wood boxes  between grow cycles would maybe help too.

I started using warming trays to hold my paper pots I use for seed starting for transplanting and I love that they're easy to carry around, easy to clean, and available in a bunch of sizes. Mike looks like he's using a large but shallow version which would be a good choice for what he's doing, but if you don't want that many greens at once, 1/2 sized trays might work. The trouble would be that the wood would take up proportionately more of the volume as you go smaller.

I do it very differently, in jars with metal screens, no plastic.