This is a tough question, and there have been a lot of thought provoking opinions so far.
Hunting ethics is more of a personal thing, based on eachs own experiences and moral compass, and doesn't necessarily equate with what's legal and what's not. 2500 acres is a pretty good size chunk of land, but there are still alot of variables to be considered.
How long has the property been fenced in, and is it actually a "game proof" fence. What's the layout of the base and how much ground is actually open for hunting? Where are you hunting in respect to the fence? Is your closeness to the fence, or it's relationship to some terrain feature [or whatnot] what's governing the animals movement?
These kinds of things, and probably some more I'm not thinking of, could have an effect on whether one thinks it's fair chase or not.
I agree with Biggie on the population control thing. If they're that overpopulated there's other people to deal with it (especially on a Guard base!). I'm a hunter, not an exterminator.
For me, I'd have to pass.