Assuming you have plenty of room to manuver to exit when you are clear of the slip, it seems your biggest concern is staying away from the other boat.
As you can see, there are plenty of solid opinions on the best course of action; here's some of my thoughts. I assume that, if you cast off all
lines, the boat would immediately drift to starboard with the bow trying to swing into the wind. You can easily check this by slacking the
lines a bit.
1. Prepare spring by taking off half hitch and additional turns to leave a turn and single wrap only. Depending on strenth of wind, this may need to be hauled in quickly from backing movment.
2. Cast off the bow and get line aboard/to dock.
3. Engine in reverse, helm to port, cast off stern.
4. Holding bow from swinging to starboard, wife walks midway between spring
cleat and stern
cleat and gets aboard.
5. As needed, neutralize helm or to starboard to allow stern to swing.
6. Keep moving. Remember your steering is very limited and the helm won't respond if you don't have water flowing past the rudder.
The tough thing about any departure with a crosswind and/or current is that you aren't really sure what will happen each time until you start to get underway. Each time is an opportunity to learn and polish your technique!