Security restricting movement of servers
Solution 1:
I wouldn't call it "normal", but it's not unknown for DCs to have all sorts of insane policies like this. From your description, the policy is only about removing servers, which makes it sound like an underhanded attempt to prevent you moving to a competitor, rather than any serious sort of security. (I'll bet their rationale is "well, if you're stealing them, the real owners will find out and stop you before you can clear the place out", but that is, of course, ridiculous -- how much better is it that their security allowed people to steal two of your servers, presumably the most valuable ones, rather than the lot?)
If you've got an account manager or any sort of "higher-up" contact, you definitely want to get onto them and start making all sorts of unpleasant noises. If that doesn't work, I'd make two plans -- one for having to do it in pieces over 2 weeks, and another that covers you being able to move them quicker.
You may be able to get more servers out by just asking the guards nicely (perhaps one particular guard isn't so hidebound), by bullshi^W
being thrifty with the truth ("what? no, I haven't taken any servers out tonight, that was last night"), doing it before/after shift change, putting N servers in one shipping box, or taking them out via the loading dock.
Finally, if all that doesn't work, I'd try taking more than two servers out at a time anyway and watch them try to stop me. It's your equipment, after all; what are they going to do, call the cops to report a theft? Crash-tackle you in the lobby in front of the security cameras? The cops are going to laugh in their faces, and they don't have a lot of other options. This doesn't work quite so well if you're planning on remaining a customer in some way, but I'd be getting the hell out entirely of a facility with stupid rules like that anyway.
Solution 2:
I've seen crazy rules like that before. Usually you can talk to an account manager or some sort of higher up that can talk to security and inform them of an exception. While I wouldn't expect them to bend over backwards for you, I would expect them to act professionally and let you move your equipment out at once.