Ah! Was looking this thread and the pic over too hastily
In a way you have a similar issue here with the inability to duct/channel the air. Plus, the open back is fine for a noisy DC or colo, but not for home.
The following might work ...
Fashion a boxlike "cavity" at the bottom (again it doesn't have to be perfect), using the UPS and/or a rack shelf. The "wings" part I was talking about... the big box stores have rubber-like sheets that are ribbed or cleated. I wish I knew what the stuff is called or officially used for, but these could be added to the shelf to help seal the cavity. I happened to have the stuff in the garage from an earlier project (commuter bike mud flaps... way too much of it left over but glad I kept it).
Side note: for that rectangular cutout at the bottom.... simply get the smallest air filter you can find (typical type used for home AC registers) to cover that. Heck, use duct tape to secure it... you now have some decent filtration!
So back to the boxlike cavity.. keep it open at the front. Install rack-mount fans there... like
these! It's a bit pricey but it comes with the thermostat. Reverse the fans if needed so the air blows out and to the front, and is forced up between the glass door and servers.
Use the blank panels between servers as necessary and let the cooler air go through and exhaust out the back of each server (and any other chassis in there).
If you can live with the noise, leave the mesh back as is; otherwise, cover it on the inside with butyl deadener sheets and exhaust air out the top (or top of the back). Redneck engineering at its finest!