I'm thinking the time of day I called paid off big time- instead of right at 10 am (I was in a meeting at work!), I called around 11:15 am and got through in about 5 minutes. They even have a pleasant little history of TFL while you wait.
I got through and was able to secure a 9:15 pm reservation for 11/30, which the very nice woman on the phone said was their last night open before renovations. So just FYI to all trying to call through for December, I believe they'll be closed, and I don't know for how long.