Any chance you could talk to base IT and see if they could maybe give you temporary access on your Xbox to download some DLC? I realize this is a very, very long shot, I almost feel bad for even mentioning it but hey, try all avenues when it comes to gaming!

This is a very unique situation. My feeling is this is how it will play out.

1) You send an Xbox hard drive (or someone buys an Xbox hard drive) that they then use on their Xbox to connect to your Xbox Live account.
2) They purchase and download the DLC and whatever else you're after
3) They send you the hard drive, and one of two things is going to happen. Either you'll be able to access the DLC offline, or you won't.

I think that the scenario that actually plays out is going to depend on the DRM in the DLC. If the DLC requires that you be connected to Xbox Live to play it, it's not going to work. Maybe you can research some of the specific DLC you're after to see if that's the case?

Also, you may look into the ability to transfer DLC between Xbox systems using a flash drive. I've never personally done it, but not all Xboxes have hard drives, so maybe it's possible.

Sorry I can't be of more assistance. I have an Xbox and Xbox Live, but I've just never had a need to delve into the scenario you've presented here.