Hi, Adriaan.
Maybe this specific string had manufactering problems, I don't know... The problem was clearer in E string, but it wasn't as the detuning effect you described, it really was an quick drop and raise in pitch. Like glimpses, if you know what I mean, or one single vibrato.
It wasn't too evident to ears, but it was strange when someone used a eletronic tuner. The needle simply looked undecided. You could take one right pitch by mean, but the needle sudenly would made that quick left and right swing.
I usually cut off highs and favored neck PU (and plucked lightly near the 24th fret), to prevent any possible harmonic interference since I read an article about that. But it didn't worked (as was useless using both PUs or the Bridge one, changing plucking position and strength or using 2nd Harmonic).
I usually am very methodic on changing strings.
I change one string at a time, usualy going from bass to treble, always leting around 2 ~ 2 1/2 inches over the post and sharp bending the string before cutting it near the bend. I let 1/3 inch or so at the end to insert the string into the post hole. The lenght slightly varies if the string is thicker because the idea is to get just 2 or 3 full turns of the string around the post (always forcing the string down on each turn to sharpen the angle string make at the nut).
I use my hand and arm to keep some tension on string while it's still loose and, after tuning all strings for the first time, I force each down and up at the middle, at the bridge and above the nut before tuning them again (and repeat before that, until they stabilize). And I always tune the strings standing still with the Bass on the strap (avoiding touching the neck)...
No, it wasn't me or the Bass, may be it was simply bad luck and I was blessed by a bad set. It can happen (sometime ago I had a string that magicaly broke when I first started to turn tunning machine, almost no tension yet).
This is why I'm asking. May be I should try one of these again... Thanks.