The label on the new battery clearly states slow charge at 120-150mA. Your JR wall wart is perfect for forming and charging that new pack, forget about using the Triton. Fast charging at 1A, as the label also shows is not as good for the battery as the slow/forming charge. The battery will give better service life if you stick with the slow charge.
A transmitter battery is cycled by using it, no need to use the Triton. If your JR 9303 has a system timer that logs the total time the transmitter is on, and can be reset after charging the battery. This will give you a decent idea as to the capacity the battery is delivering.
Sadly, the RC hobby is a mess as far as connector gender goes. Regardless of what anyone in the RC hobby thinks. Gender is always determined by the contact, not the connector housing. I started with a Futaba radio many years ago that used the old G connector, that really was male, so how can a modern servo connector be male
. Think about it
Pete