I recently purchased a new 594 with the new tweakable Phase III tuners with the dual set screws on the collars & I was having tuning problems too. The tuners shafts were very loose, so I suspected they were slipping. I finally located an Allen wrench that fit the set screws & was able to tighten the collars which tightened up the shafts. That fixed the problem & it stays in tune much better now. Prior to tightening the collars, I lubed the nut with graphite grease & stretched the strings ad nauseum, which didn’t help. The wrench size is .89mm & the cheapest I could one was online at Chads Toolbox, made by Bondhus I believe. 29 cents per wrench + $6 shipping. Bondhus appears to be the only manufacturer of this size wrench.
BTW...the Phase III tuners are definitely made by Gotoh & some of the worst I’ve ever used. That’s who told me the wrench size & wanted to sell me one for $3 + handling + shipping for a tiny Allen wrench. They’re very rough (not smooth over the full travel) after adding tension on the collars. I have stock, non-locking Klusons with the plastic Keystone buttons on a Historic Les Paul & custom shop 335 that are much smoother than the Phase IIIs & they don’t slip. I had an original McCarty, a Custom 22 & an SC250. All of those guitars had rock solid tuning & is one of the reasons I bought 594 online without playing it first. PRS guitars have a standard of excellence unbefitting these tuners. Yeah they look cool with the open back & low mass, but.......... It’s a sad day when a Les Paul & a 335 have smoother & better tuning stability than a PRS.
Some other info on this forum in a thread I started suggests using a .035 or 9mm wrench. I’ve tried both sizes from a wrench set made by Tekton, but they’re not a good fit. The Bondhus .89mm is perfect, with no wiggle room to strip out the screw heads.