Yes TarX if left to dwell would have most likely conquered sap.
This is interesting looking:
It has the look of rail dust, yet it doesn't in parts. So, I'm slightly baffled...
1. Can you feel these marks at all with your nail or a your "plastic baggied covered hand"?
2. I'm wondering what an aggressive claybar/alternative would conquer...?
3. Have you considered polishing?
This almost looks like overspray of some sort. Something that may have settled on the paint and embedded itself into the pores. Kind of like solvent based tire dressing sling....however sling stains are a faint yellow color. These stains I'm talking about tend to be permanent; your issue doesn't look like this, but does make me wonder if you're dealing with the same concept.