I don't know about the Houston area, but the FP are done in 42 days from the day you call. So right now even I am for the Atlanta area I am, basically, scheduled for the same time of you.
In other forums and discussions I read that are people that get 2 days before or something like that, at their risk, to the office BUT it depends of the officers or the guards at the entrance when they ask you for your FP notice, which is no guarantee of anything since they will know that you are not schedule for that date.
To try to get an appointment early...uhm I guess you can continue calling to check out if there are cancellations and then they can book you in an early date I think.
good luck,
