With dremel and cutting, chopping you risk ripping pads off, no matter how delicate you try.
Just use heat gun, place kapton tape on things you want to stay on board, use heat gun from connectors side to heat both pins and metal frame, after you got it out, put some solder on pins, wick solder out, put new one and use soldering iron to solder first metal frame, then pins. If you happen to make some bridges while soldering, use wick to take those out. Connector will melt? Who cares, it's broken anyway.