TNG "Family" is our best source so far. Jack Crusher's holomessage with the TWOK uniform is dated at Wesley's birth, hence 2348. His uniform came to feature TNG-style collar pips before his 2354 death, though, as Wesley inherits those.
It seems reasonable to assume that Jack's pips came from after
the uniform switch, which in itself must have happened after the holomessage was actually recorded.
I think that nails it down to my satisfaction. The uniform change must have come sometime in that six year period. And given that TNG begins in 2364, that gives us around 10-15 years that the TNG uniforms have been in effect before "Farpoint", give or take.