@malutki: thanks for your response :-)
Apologies for littering once more in your polite forum - I'd like to report the resolution of my "trouble case":
After some time wasted by investigating my various options, I decided that my time was too precious for this and that I should spoil myself once more... and "bought my way in". I bought a new absorber, the McLeod by Manitou. And... even considering my instinctive need to justify the money I spent on it (and hence my positive bias), the McLeod seems to work great. It appears to be the cheapest shock absorber on the market that allows you to adjust both rebound *AND* compression, by two independent dials/levers. And of course the spring rate (air pressure). So my first interest was to dial the compression damping to minimum and... and it works. Oh the filthy feeling of a floating tail :-D Finally. Finally the rear suspension seems to work "the way it has always been supposed to work". (Now the front fork feels comparably a little stiff, but I have to be hard to myself. I don't want to shell out another 200 EURO for an air fork. I'll take a look inside the Manitou Match Comp, maybe it just needs a cleanup.)
Thanks for your attention :-)