You have an S+ MPU.
You know what?
You said earlier that "you're afraid to get it too hot and screw it up"...why not just solder your new battery right to the leads of the old battery...then cut OFF the old battery right at the ends where its leads go into the body? You may save the memory programming too!
Just make sure you have the positive terminal in the same orientation as the old battery....which by the way, is the top terminal when the board is standing up in the machine.
To understand which way is "up", the two long white connectors with a million pins are at the bottom of the MPU, and plug down into the motherboard.