We talked with a few other teams and even went as far as to use another team's copy of Labview on their computer to see if there was any difference. Booting the Crio in safe mode, playing with IP addresses, and replicating the problem on 3 different Crios with 3 different computers leads us to believe that it is a problem with Labview 2013.
A minor breakthrough: tinkering around with the NO APP switch allows us to download code, which was the first thing Mr. Anderson mentioned. (Thanks, Mr. Anderson!
) It doesn't affect the underlying problem, though. It still takes significantly longer to test and deploy than last year which may or may not be a problem come competition. Hopefully an update will be rolled out by then.