Well there is no API anywhere other than NASP, so sending people to Vance wouldn't help any back-up at NASC. So that doesn't make any sense.
To the OP, when I was in A-pool we were explicitly told, "If you want to go TAD somewhere, let us know, it's no problem." I waited about 5 months for API, 1 week for Primary, and 2 months and counting for advanced. Bottom line: talk to somebody there, in person. They'll be able to answer better than most of us on AW can.
Also, generally a new class starts every Friday, not one Friday a month.