Thanks for all the info!!!
I'm surprised that my first post could start such a discussion!
Anyways, since I'm a PhD student and I'm working here, I surely cannot leave to FL for three weeks to take a JAA licence (I just found out that around NY there are no such schools)!!
My VISA lasts for the next 3 years, but what matters is actually the I-20 which lasts even longer (no problems with the duration of stay instead: indefinite). I would be kind of reluctant to change VISA status or similar things, since it could really screw things up badly, especially if I do it without informing my home institution...
Well, I think that at this point, the safest thing is to contact USICS and see what they say! I'll update this thread once I have an answer.
Cheers!
Ale