Does anyone recognize these telephone and television DEMARC boxes or know the manufacturer?

They're exterior rated boxes that are open in the back and have a plywood mounting board inside.

I need to come up with a matching set for a project, but won't be back onsite in time to open them up to look for manufacturer/part number:

Guessing Benner Nawman: [Link: benner-nawman.com]

I believe you're correct. I haven't pick one up in a while but I get them at Graybar Electric.

Those don't match the ones in the OP's pic.. Says he needs a matching set.

If you read at the bottom of the page, it says they can be ordered with standard embossed & custom embossed lids (like in the picture).

Looks to me they are very similar to the ones as well.

I have to agree that is the best match. But, the picture from website is a generic early picture while product was being developed does seem to mount over a four sides of the enclosure vs the OP picture showing the top of cover going under a lip.
Send picture asking Benner Nawman if it is their product.

Thanks guys! I'm digging around more this morning and found one from Westgate that might be it or a little closer than the Benner Nawman:

[Link: westgatemfg.com]

[Link: westgatemfg.com]

I'll take some photos by Graybar to see what they have.

I've seen a TELEPHONE version of this, or something very similar, that's about 4" high, at Home Depot, of all places!

As to its mounting, these are usually not mounted as the first photo shows. The plywood is nailed onto studs and stucco is built up around it, leaving about an inch of the box sticking out of the stucco. This, with their shape and lid construction, keeps water out of them.