Right now, JPA is getting to 3 ball counts at close to league average rate, so I'm not sure he needs to go to the minors to be fixed. The real issue comes once he gets to 3 balls. On average 41% of the people that get to 3 balls in the AL this year draw a walk, while JP is only at 16%. If JP drew the walk ONCE GETTING TO 3 BALLS at a league average rate, he'd have 10 more walks on the season which (without doing the math) would probably raise his average about 10 points and OBP by 40 to 50 points. That's without him changing ANYTHING else. Combine that with the fact that's he's in a slump right now (probably partly due to overuse), and I don't see major adjustments that can't be made at the major league level. Just one tweak in that thing he calls a head when he gets to 3 balls.
Some of the other things would be nice (and should be worked on), but just that one change probably puts him back to where he's at least a partial asset to the team.