If it were me, I would go to the collective and would not recommend LAMA at this point. It does a bit depend on a) what you mean by jazz and b) whether you'd rather end up in LA or NY, if you were to stay in the USA.
LAMA has gotten expensive and the collective was already pretty expensive.
I used to work at LAMA and i know the folks at the collective pretty well, so feel free to PM.