Almost. You will probably also have to clean the SMS adapter's GG pins from solder before you can put the connector in.
As for your point 2. (the GG connector unsoldering), I've done this once and it was a real joy thanks to its long and flexible pins: I managed to get it out only using a heat gun.
a) Remove rivets that nail connector to PCB
b) Cover bottom side with alu foil, leaving only solder points exposed
c) Pad gap between connector plastic and PCB with paper to obtain some tension
d) Gently apply heat from below until solder melts and connector loosens
Repeat steps c) and d) until connector falls out

ad 3., if you don't mind using the plug-in naked (PCB only), of course you don't have to ruin the shell.