I'm in a situation in which I can't compromise any walls, but can instead mount an external box. I know something like this could be made fairly easily, but the problem is, I'm fairly inept, don't have the proper tools and would love to find an already-made solution. I've searched and searched and searched, but I can't find one. I think something like this has to exist, but I just don't know the proper search terms.
I guess the closest thing I can think to what I need would be a small fuse-box style box, but instead of switches in the front, a wall-plate mount in their place.
Wall-Mounted Box for Wall Plates (Cannot Compromise Wall)
What you are looking for is called a "two gang" box.
Your problem is going to be finding one that is 4 inches deep. Most surface mount boxes go up to 2 1/8 and most that are intended to be inside the wall stop at 3 1/2.
I looked at your link, and I am wondering if you need the full 4 inches. The devices you show, look like they are made to go into a standard box. In that case a "two gang" "wiremold" box will work.
Wiremold is a name brand and they have their own web site under that name.
You can also check out the RACO web site for metal boxes. Most can be fitted with a two gang "decora" cover that will let you mount your devices.
Some companies make a 4x4x4 "junction box" that you may be able to fit a two gang cover to somehow.
Another option is to take a trip to a local electrical supply house and see if they will let you look at what they have in stock. Be prepaired to wait around if they are busy. Nothing happens quickly at a supply house. Remember everyone else there is on the clock.