Lots of excellent replies to this thread from everyone.
I have experienced this issue on an instrument (not my own) before, but it was so many decades ago, that I can’t remember now how it was fixed.
But will try so here are just a few thoughts.
When problem solving, it’s helpful to determine whether the issue is simple or complex at a very early stage.
I do wonder whether the difficulties eliminating this issue is because the problem is actually caused by a number of quite different factors, interacting together simultaneously.
Therefore, it may be necessary to approach the issue with a view to regulating a number of differing elements that require adjustment or even replacement to fully resolve the problem.
In short, complex problems usually require complex solutions.
I did wonder whether the action is on the low side for a fretless bass?
Its not uncommon for players to desire a lower action than is ideal for the calibre of instrument.
Could the combination of a low action and high-power magnetic pickups be interacting together deleteriously?
So, raising the action and lowering the pickups quite drastically to real extremes would be my first adjustment, purely to make an observation about.
If those dual adjustments eliminated or massively reduced the issue then its possible you might need to come to terms with adjusting yourself to a higher action, more typical of double basses, and perhaps rather less aggressive magnetic field pickups as replacements might be necessary, to completely remove the issue altogether.
Test, Try and Prove.
As the issue is more evident the higher up the neck you play, it is more likely the pickups will interfere as the string is vibrating closer to its pole pieces.
You are striking the string sideways but too strong a magnetic pull may be inducing an additional directionality to its movement creating an unusual sonic artefact.
Seymour Duncan What is "Strat-itis"? - Guitar Pickups, Bass Pickups, Pedals
What is "Stratitis"? (sweetwater.com)
Just..
Check that the saddles are not flat and indeed the nut grooves, and put some foam or wad of cloth behind the nut for good measure to eliminate their vibrations.
The string must rest on points, any flatness can cause unwanted phasey sounding buzzes.
Contra wise, too deeply notched saddles (or nuts) can be home to similar phasey sounding issues.
String interference, where behind the nut, the end of one string sticking out from its tuner, touches another string as it passes can cause issues.
It’s unlikely if you have the problem on all strings, but easy to look for and eliminate.
Likewise at the other end, look for securely seated string balls.
Is the neck adjusted correctly?
It’s been tightened so as its settled is there any kind of back bow that is causing the string behind where you are fingering to sympathetically vibrate and create a doppler type of phasey effect?
I think that’s highly likely and in combination with too low an action and too strong magnetic pickups, might actually be it.
Please don’t imagine I’m trying to be controversial here, I’m not looking for an argument, just exploring ideas.
When I started in the music business (a very long time ago) the widely accepted conventional wisdom was to look for a completely straight neck in a stringed instrument.
Over the years the widely accepted conventional wisdom has altered (but not for everyone, including very esteemed individuals both luthiers and players) and in general, people like prefer to have a degree of relief.
Whatever you think its o.k. with me!
Anyway, a few months ago I was thinking about all this and rang up a relative of mine who is a violin maker and repairman, often sought out to work on very high-end instruments, Stradivari etc.
I was wondering how he approached the subject of straight versus relief, on such fretless instruments.
I thought I might learn something, and did.
He explained the ebony fingerboard is set straight and then he planes (and has special little planes set up to do this) ½ a mm of relief on the treble side to ¾ of a mm on the bass side.
If he introduces such relief of the violin family instruments (and works on Basses Cellos, Violas etc.) then it’s probably genuinely important to have a proper degree of relief on fretless basses in particular.
Although the luthiers that you are dealing with might be experts at fixing fretted instruments and their problems, its highly likely they are far, far less familiar and experienced with fretless instruments, and completely unacquainted with the issues that can occur with them.
In short, the tightened neck might require better relief, and this could help eliminate phasey effects from behind the fingered point too.
So, a properly sorted neck, in combination with a higher action, and lowered or replaced pickups, as long as there are no issues with the saddles or nut affecting the strings vibrations could be the way to eliminate this issue.
If the new strings are worse, this may be to the normal brilliance resulting from their newness. Are you boosting treble on the bass or amp which could be exacerbating the effect, which the newness of the replacement strings also boosted?
You are highly sensitised to the effect now, so give your ears a break, and try a flat E.Q. to start with when you play and see how you go. I will be surprised if the problem is not two or three of the possibilities mentioned, possibly more, interacting together to create the unwanted effect.