Congratulations on your 306 SACD. Your CD player should be well burnt in by now.
Do you have the original 306 or the newer, updated "Mk II" version? The newer version has an updated logic board and a new digital section. I had my dealer perform the upgrade. There are several nice improvements - the CDP reads the TOC of RBCD and SACD faster. All the bugs have been ironed out (no more random hangs or power offs). And the sound has improved slightly.
The two most effective tweaks I have performed are (1) cover the window on the top. I just place my CD cover on it when I am playing a CD, so this is a free tweak. (2) Place the CD player on a granite surface. I have tried a wooden chopping block (hey, it was free!) but did not like the results.
I cannot comment on the power cords as I have not tried them. I could probably "borrow" a nice power cord from one of my other components but then it makes comparisons difficult! Good luck with your quest and please let us know what you discover.
Cordially yours from sunny Australia, Keith.