Adding onto this: I've also noticed, if you play multiple different characters during a match (or across multiple matches) before returning to backyard, this method above only 90% guarantees the LAST CHARACTER YOU PLAYED saves.
In one of my matches, I leveled up my Toxic Rose to Level 10, THEN leveled up my Fire Rose to Level 5 in the same match, and when returning to the backyard the Fire Rose Level 5 saved, but not the Toxic Rose Level 10.
So to add onto this, its also better, especially if you are going to play multiple matches in a row, PLAY THE SAME CHARACTER EVERY MATCH, or at least end your final match playing the character you most want to save. It seems like this server bug is causing the backyard to only remember the levels of the latest character that you played.
However, on a brighter note, this method above has worked nearly 100% of the time for me, and I also have not needed to wait 15-20 seconds. I just leave the match right when the character select screen shows up.
