I see that as you having one exceptional bass, multiple exceptional basses, or a very good tolerance of changes in playability.
I've changed strings on basses and the result was me being virtually unable to play the bass as I had played the bass before the string change. This was usually when making a significant gauge change between strings. It wasn't always that the bass became totally unplayable, but it became so difficult to play, I couldn't play some passages on the bass with the new strings without making adjustments.
I've changed from heavy gauge strings to light gauge strings on several basses through the years and nobody could play the bass afterwards because the strings were laying on the frets.
I have several basses and some are much more tolerant of string tension change than others. I have a Carvin 5 string that never needs the TR adjusted as long as I stay with same or similar strings. I have a Gibson TBird that needs the TR adjusted a 2 or 3 times a year with NO string change, unless a person is very tolerant of fret rattle or high action (it drifts between the two with humidity. change).
Due to the type of bass the OP has, (hollow body), and the notable high tension of LaBella flats, he or she might have a Frisbee practice target after installing the new strings (as in the ability to throw a Frisbee under the strings). In those cases, a setup isn't overrated, it's a requirement.