My experience Flying HAV-PTY-JFK
I have flown Copa Airlines Hav-Pty-JFK
3 times this year and upon arrival at JFK
US citizens were processed via the Automated Passport Control (APC)
all you do is scan your passport, have your picture taken, click yes or no to the usual questions on a paper customs form
and a Ticket is then printed (Looks like a Boarding pass)
all the printed ticket list is the flight you came on and airport
which would be PTY.
After baggage claim you hand this ticket to an officer as you exit and thats it.
Never had any questions asked or anyone look through pages of my passport.
Yes Cuba has been stamping all passport in recent months,but they will usually comply if you request them not to.
I have a passport full of cuba stamps.
This has been my experience and that of my travel companions.
I would not be so worried and simply enjoy your trip
Ps: If asked directly its a Federal crime to lie to an CBP officer so I would suggest you dont. I think the chances of this happening are close to zero unless youre acting all nervous and suspicious.
Happy Travels