I dove with LK twice. Picked them for price. Was new diver 1st time. Very disapointed. Tried again years later, again disapointed. tried Cris Sawyer 2 years ago and found what a professional op sould be . You get what u pay for.
just my 2 cents

I take it for granted that your Delta flight arrives JFK and not LGA. 45 mins, to me is not enough time. Security lines and the size of the AA terminal would make me re-think this. Another option would be to come to JFK the night before and spring for a hotel. Wake up at 6 AM and shullte to the term...

you can always check in with your airline early