I was able to take the GRE subject test on standby this past Saturday! I might start a new thread on this for anyone who's in a similar situation, but for now, I'll just post it here.
I purposely went to the testing center with the lowest population nearby but which was still within a reasonable proximity to my location. The reason being, when I called ETS, the woman on the phone advised me that the testing centers in lower population areas tend to have more availability. This turned out to be wholly true, and I was, in fact, the only standby test taker at the center I attended in New Jersey. To any future standby testers: don't sweat it. If you go to a testing center away from major cities (even if you need to drive an hour it's worth it), it should be a piece of cake to get in. They had a ton of extra packets for all subjects where I went.