In a previous (and last) attempt, I mounted a Stetsbar tremolo on my "Black beauty" Fernandes Monterey Elite.
I removed it. Not because the tremolo is not good, but because of another feature that I added: an Hipshot tuner to detune the lower E string from one whole tone. This is totally incompliant with a floating tremolo. Moreover, whatever the fine tuning, Black beauty was always out of tune because she's in D (all strings one whole tone down). The Hipshot tuner goes to C-drop tuning for heavier sounds.
As far as I can remember, I was always unhappy with the tune of Back beauty. Some chords never felt right, the F (ex-G) string was always wild, and playing high pitched notes was adventurous.
I add to find a solution to set the harmonics right with my 11-48 gauge tuned in D! Tune-O-matic bridges provides too few settings to set strings perfectly right. The bridge is never tilted enough to my ear and the saddles do not go far enough.
But one glorious day, tadaa ! I found THIS ABR-1 BRIDGE.
As you can see, on each side of the bridge, you have small screws to tilt it right: more string length on the lower D (ex-E) string and the upper D string can be shorter. Moreover, saddles have more range than a regular Tune-O-Matic bridge and they are equipped with brass rollers which gives more sustain.
I mounted on my Black beauty and honestly I can say: THIS IS A (R)EVOLUTION! This marvellous guitar is now perfectly in tune, whatever the position. Chords sound right! The F-string is now OK (except the very first case, as always...) and the sustain... Waow, now she sings!
So, this is my advice: whatever the guitar that has a Tune-O-Matic bridge, always upgrade it to keep it in tune with a right harmonics setting!