Funny how things work sometimes
I was referred to Frets.com in an unrelated thread. I've known about the website, but didn't think i'd find the particular problem/solution there.
still, looking through "buzz diagnostics" i found one potential reason for a dull string: a loose tuning key! The thing is: it's hard to notice if it's loose unless you remove the string.
Sure enough, they were all loose! I tightened them (both, the screws on the back of the headstock and the hex-nuts on the front). I would never even guess that, because the tuners are beyond the nut and who would've thunk that they can affect tone?
I should also point out: the old trick about twisting the string a few times to "tighten" the windings - I may have been overdoing that, which also contributed to the problem! I would twist is 5-6 times, as much as I physically could. Now I maybe give it one twist. I'm guessing that this trick is perhaps "outdated" - quality strings probably don't suffer from loose windings.
So now my bass sounds fantastic with Martin SP mediums - it's nice and deep sounding, but also "modern" (like an electric bass) and even sounds great for slap/pop (not that I play that way, but I sometimes just mess around).
I am glad I haven't given up! This bass is a great deal after all.