GE kiosks allow you to manually enter your flight details if it fails to locate your Secure Flight information. I would advise going to the kiosk as normal and checking to see if it automatically recognizes you. If not, simply type in the requested information and it should clear you per usual.

Failing all of that, the worst case scenario is that you have front-of-the-line privileges for normal clearance by an officer.

I assume the CX flight from JFK is your originating flight, so the lack of Precheck isn't an issue.