You can get a cart in the arrivals hall inside customs while waiting for your bag to come out. They cost ~$5 (cash or credit card) and that should make it much easier for you to get from T4 to T5. You can keep the cart all the way from when you pick it up inside customs to when you drop the bags back off with jetBlue in T5, including on and off the AirTrain.

The security thing was going to happen again no matter what so no real choice there.

Keep in mind that you will be charged for the second checked bag on jetBlue.