There are 100's of individuals who are more qualified to answer this question (most of 'em are named Brett and/or Jones), but I'll give it a shot since shoulder mobility tends to be my limiting issue. Smart people please correct me if I'm way off.
Have you been put through the FMS screen to assess if your shoulders are , in fact, your weakest link? We can only guess from what you're telling us that shoulder mobility is your biggest issue; however, their may be other limiting factors as well. (hip, core). The FMS screen will show you your current movement baseline as well as expose your weakest link. It may be shoulder mobility, then again, it may not be.
If you've got limited shoulder mobility then KBS may not be the program for you. Again, I don't know you personally, so please don't take this as insult to your experience. Which programs have you completed recently? In other words, have you spent quality time with swings, get ups, and single KB work in order to progress to doubles? (which is a whole new beast w/in itself)
I didn't see much improvement in my own mobility issues until I went to a chiropractor who specializes in Graston, Active Release, FMS, as well as SFMA. He cleared most of my tightness w/ hands on therapy ( that felt like Medieval torture at times) as well as Rx corrective exercises to help me regain acceptable range of motion. Again this is just 2 cents coming from a dumb Texan fire fighter .
Hope you find the answers you're looking for. Best in strength.