Reporting back;
I gave wet and dry sandpaper and Novus 1,2,3 multiple thorough attempts. I used them independently and together and on multiple boards.
There was little overall difference unfortunately (blue and grey boards btw).
(Strangely enough, none of my green boards have the discolouration at all).
If I had a buffing brush for my drill I would have attempted that as well. Hard to say if that would have made a huge impact - as it does indeed seem like the marks are discolouration and not merely surface stains.
+1 for painting over.