You may have more than one pest. That does not look like mites alone. Mites build messy 'webs' on the UNDERSIDES of the leaves primarily. The webs contain tiny pearl-like eggs that are visible to the naked eye. The damage they cause looks like the overspray of white spray paint on the TOPS of the leaves, most pronounced in the warmer part of your grow room, and on the stinkiest plants.

The fecal material on the tops of your leaves, along with the description, makes me think you have a second bug in there.

Don't move those to the shed until you treat. Bomb your veg room TWICE with a pyrethrin-type bug bomb. There is a pyrethroid product that Raid makes in a yellow and blue package. I've seen it at Home DePOT. Follow the directions on the package, and repeat again in 3 days. Bomb the shed twice before putting the plants in there. You will need 2 packages because each only contains 3 bombs.

Apply a light mist of neem oil. You can find neem at home depot as well, sold under the name 'Fungicide 3'. Raise your lights. Allow to dry. Wait a day. Mist lightly again. Repeat until the leaves take on a slightly more glossy appearance. Neem oil is not only disgusting and distasteful to common pests, causing them to stop feeding, but it also prevents the plants from losing moisture through the damaged parts. IT CAN suffocate your plants if overapplied, so mist lightly and watch for signs of darkening of the leaves.

Good luck.