Hi Andrea.
First question: why did you change out the bridge? PRS hardware - even on the SE line - is carefully designed, well engineered, and pretty well quality-controlled. Musiclily, on the other hand, is lowest-possible-price bargain gear that often looks like the thing it's supposed to be, rather than actually being it.
The PRS tremolo has a specific and functionally important relationship to its 6 mounting screws, in that they're factory-installed to a precise specific depth so their top grooves provide a consistent fulcrum point for the tremolo body. Disturb that relationship, and the trem gets unstable. Installing a different brand, you defeat all that, so you'll have to be diligent and persistent in fine-tuning the depth of all the mounting screws to get similar consistency. (And it'll take a good bit of intelligent guesswork and/or luck as well.)
That said, tuning problems, with or without tremolo - on any guitar - are only sometimes (and then pretty obviously) caused by the trem itself. And it's even more rare that problems are caused by the tuners, or solved by locking tuners. There are exceptions, of course, but it should be chanted like a religious mantra: it's the nut. It's usually the nut. It's almost aways the nut. When a string doesn't return to pitch after whammy action, it's 99.98% certain to be the nut.
The PRS nut comes in for a lot of abuse, but I find that if the string grooves are widened a little (and sometimes tapered down more toward the headstock), it works well. I also have an SE, bought used, that came with a Tusq XL nut - and guess what? It was badly cut (no way of knowing by whom), so that it grabbed strings during tremolo use, deadened a couple strings due to a bad string path across the nut - and hadn't been cut deep enough on several strings so that action suffered in the first few frets AND caused low-fret notes to bend sharp. I worked on it; now it's fine.
Moral of that story: it matters less what nut is on the guitar, than that the nut is properly cut and dressed. It's probably the most crucial job in the setup of a guitar, and the hardest to get right. Until recently, I've always been happy to pay professionals to deal with it for me, because there's nothing like a bad nut to turn a musical instrument into a wall-hanging. I bought a set of files and lately have been working on them myself, with pretty good results and no disasters. Yet. But if you're unsure that your Tusq was properly grooved and dressed - and don't do such work yourself - it's probably worth paying an experienced tech to work on the nut, and address all the components involved (tuners, nut, bridge) as a system.
I'm also jealous that you got the Santana Standard with the binding. Beautiful guitar, especially for those of us who have a lifelong love for all-mahogany bodies. I'm on the hunt for one...and was following the only 2018 Standard on Reverb, which was in Italy. It sold. Did you get that one?
