My idea for a JFK branch from the BR line in Caransie would branch off at E80th Street, which happen in region R on your map. Also in Region R, the JFK branch would turn east at Seaview Ave (From E80th Street) and go straight down that path, though region P, where it would make a right, alongside the line and end at JFK, it would run along side the Belt parkway once it turns at Seaview Ave pretty much.
The 86th/4th idea can be axed as I see if doesn't go into a shaded area.
The LGA Airport idea, it would use the Bay Ridge line tracks from 5th Ave in Brooklyn up until Northern Blvd in Queens (In region I) where it would branch off the BR line and follow the BQE to GCP to LGA Airport and there, also in region I.