Finally got it, as the topic says. The strange part and what is still confusing me is that the last steps towards my goal were exclusively done on MP servers (the last step was on Olympus, decreasing Guild reputation down to 7%, [Tranquility, Pearl]). From my understanding (and from what Vice has said) faction reputations should NOT carry over but in this case they DID, no matter on what server I was. It always carried over and in both directions (SP<->MP).
Once more: I'm NOT talking about overall system level, which I meanwhile understand is static on MP servers (and of course still hostile on all MP versions of Pearl).
But as a result of the carried over faction reputations my SP version of Pearl is now 'good'!
The system reputation shift was immediately there, right after loading my profile in SP.
Enough has been said (from my part), now it's your turn. How was this even possible?