All of my SWUs have been on TATL flights so not quite the same. But what I can tell you is that in the 3 years that I have been EXP I have only ever had a SWU clear outright once. All others have been waitlisted, but cleared anywhere from one week to several days in advance to 'at the airport'. It helps also if you are traveling alone as they don't need to find 2 seats for you. I remember being at CDG on a VERY full flight to DFW and clearing at the last minute in the AC because I was traveling alone and there was one seat left.

VERY IMPORTANT - if you still haven't cleared by the morning of departure, get to the airport very early and ask to be put on the airport upgrade waitlist. The reason I say this is important is because they don't automatically put you back on once you check in, you have to ask to be put back on. Priority for this waitlist depends on your check-in time.

Some routes are easier than others (IME I have found fewer EXPs leaving out of CDG than out of LHR for example).

Overall my success rate has been about 80% I would say but that is somewhat skewed because I have often asked to be put on the waitlist only a few days before departure. Even back when I was PLT and using miles and co-pay I cleared about 80%, so you definitely have a very good shot. Good luck!