Preface Edit: I do not believe "Synthetic Modulation" exists in the music theory lexicon.
I had to look this up, Wikipedia "In music, a synthetic scale is a scale which has been derived from a traditional diatonic major scale through the alteration of one degree by a semitone in either direction."
Modulation usually refers to taking the same scale, but transposing it to a new tonal center. However the term "Synthetic Modulation" is a new one to me. It sounds like you are inventing your own harmonic system, which is a fun thing to do.
In any event, I would vote for #1 "The same synthetic scale is moved from one tonal centre to another" since this is how the term "modulation" is typically used in other types of music. Modulation can also refer to changing scales, for example from major to the relative minor, but modulation often means using the same scale on a new tonal center.
2 "A change of synthetic scale whilst the tonal centre remains the same" would be like modulating from C Major to C minor, which is less common, but possible. So your term "synthetic modulation" could also mean #2.
3 "Two or more synthetic scales on the same tonal centre". This would not be an appropriate use of the term modulation.
4 "The same synthetic scale on two or more tonal centres" This would be referred to as polytonality, not modulation.