It's secondary to your problem with the Xbox but it's critical for fixing it. Something must be wrong with that hot air station, it should be able to melt the solder. Do you have a suitable thermocouple for your MM? If so, check the temperature of the hot air. If not, see if you can get hold of that IR thermometer or buy one, they cost next to nothing.
Check a few videos on using hot air, just to see if you've got the technique down and don't cook the board in the process.