+1 on what chino said. Oks naman yung stock tuners, even for moderate trem usage. Replace the nut first, nandun usually yung tuning problems. Parang pang-9s ata setup nun eh, once I went with 10s sa string gauge, grabe yung 'ipit' sa nut. Pwede mo rin file yung slots, but if you don't know what you're doing, take it to a luthier na lang. I went with a PRS nut from magdon music, which uses the same material on US PRS guitars (SE nuts on the other hand, are plastic), but it cost me 30$ total.. with shipping almost the same cost as the nut itself. You can get cheaper graphtech nuts from masterchoxter that are also self-lubricating.
Once you take care of the nut, but still need locking tuners, schaller m6 is the usual recommendation sa prs forums.