I have hankering around with the idea of 531 and gymnastics for awhile since playing around with 531 in the summer. It would be more gymnastics than PL for me as that is my focus. I was going to implement the 531 to maintain a minimal amount of barbell lifting into a manageable schedule.
Basically simple 531 without accessory work. Maybe some dumbbell/croc rows. I used to do these when I first got into lifting before they became croc rows and loved them.
I was also going to put in some oly lift work. I think I was going to limit it to one lift per day, then the 531 lift. I'd like to get my lifts better and this is more of a just for me.
However, the primary focus will be GymnasticBodies programming 4d/week with some basic event work. Not much right now as I just need to get back to basics aka making things not hurt any more.
I'm also going to keep my days off as days off and not just a day to 531/oly. I once tried to do other programming, such as light GPP stuff on my off gymnastic days and it sucked for me.
Andrew, you are on a pretty good track. It looks you are doing the gymnastics as an accessory and just the statics right now. I would hold off on the back lever work, working basic skin the cats and ring support in either a pushup or standard ring support (or assisted).
Besides the front tuck levers, I would work on the basic hangs and doing shrugs in these hangs for shoulder health.