Okay so while PM'ing with a fellow forumite, I mentioned that I want a decent fretless. He then reminded me that the Palmer I have is, indeed, a fretless. And it is a good bass. I was going to say: "considering what I paid for it (EUR 120, including delivery from Germany)" but in truth, it is a good bass. I have played a few gigs with it and did not get any complaints (probably because no one noticed it anyway).
Now, the thing is: the neck is not lined NOR are there any side dot inlays. It also came with round wounds and they have been eating at the fretboard a good bit. Pick-up wise, I am still at a loss as to which knob actually does what: they ALL seem to be volume for some reason. The signal is pretty weak and I have to rely on my amp to get good tone. I know, this does not sound like a good bass, does it? But despite its very narrow string width (it is a 5 string) it has low action and a very "fast" neck.
So I was thinking about some modifications, more specifically having the fretboard replaced by a lined or at least side-dotted finished fretboard (or an unfinished one and buying flatwounds) and have different pick-ups installed. But then I started wondering whether all this will really make "the" difference. With Squier pumping out good quality low price basses these days, I wonder whether it would not be cheaper to simply buy a new fretless, than to tinker with the one I have.