I modeled an enclosure yesterday evening, and much to my surprise, everything fit perfectly on the first try!

The IR LED fits through a large hole allowing it to be aimed anywhere from horizontal to vertical.  There's a small window for the IR receiver, and a light pipe made from a piece of 1.75 mm T-Glase filament to show the green LED (simulated in the picture; the camera flash completely washed it out).  The USB cable is only used to provide power.  The two halves of the enclosure just friction-fit together, so it's easy to get the guts out for re-programming if I ever need to.

I could go a bit further with this project, designing a circuit board and writing complete build instructions.  But I really don't know if anyone else wants a device like this, since usually a universal remote control is a perfectly good solution for consolidating several remotes into one.  So unless I see strong interest in polishing up this project further, I'll just call it complete.