Soreness should go away with the right volume. If it doesn't go away within a couple days then like Garrett said you're not recovering well. Looks like your diet, sleep and stress is all pretty good, so the biggest factor it probably will be is your training along with possible adrenal fatigue. If those are heavy DLs coupled with the squats that's probably what's doing it.
Go back to a bare bones model (aka SS or modified SS) and then work from there. If you want sub some of the upper body strength work with gymnastics work (or you don't have to). But no more. Eventually, after you're body is used to it you can spread out the volume across 4-5 days better.
If you don't want to do a linear progression I would suggest with starting with 1 legs, 1 push, 1 pull for 4 days a week and then moving up to 5. Then if you can handle that (after another few weeks) add in another push/pull exercise.