I had the same spinning problem when I was going through AFF. Any idea what's starting your spins, and what's preventing you from stopping them?
I had to repeat several levels of AFF, and a couple of them more than once... My DZ sent video up on two of the jumps for free and used it as a teaching tool. My big problems? Uneven legs, not exerting positive pressure on the relative wind, and not being relaxed.
Toe taps fixed my uneven legs. Once I started spinning, I would stop if I just arched as hard as I could and relaxed, BREATHED. Relaxing up there is hard when you're new! Well it was for me anyway, and it sounds like it is for you, too. My instructors told me to take an extra second when I looked at my altimeter, take a breath, arch, and relax. That helped a ton. What also helps is realizing you actually have a TON of time up there to work with. There's no need to get stressed and try to rush through! Just breathe and do it at a steady, even pace. Don't get overwhelmed :) If you mess something up, take a breath, fix your arch, and try again. Don't ever try anything if you're not stable, because you'll just be stressed and it won't turn out right. Take that extra second, breathe, stabilize, THEN try again. Taking that extra second will save you time in the long-run, because you won't be repeating manouvres.
Where's your home DZ? I see you talking about going to LA for a windtunnel, and I'm curious if we're jumping at the same place. AFF 1: $320
AFF 6: $850
Beer: $36
Not having to wear the bright blue spandex student jumpsuit because it's the only one small enough to fit me: Priceless