Are they running single-track through JFK or something?

Note: I don't actually know.

My assumption has been that soundbound Braintree trains turn around at JFK and become northbound trains. Braintree passengers then switch trains at JFK.

To me, this then makes sense why there's a delay: the southbound Braintree train needs to then switch tracks to become northbound. I have no idea if this is done south of JFK (i.e., it does a pickup at JFK) or north (and it skips JFK or backs into the station?). Either way, this causes a disruption, so headways are lengthened to accommodate it.

But see opening caveat. :)