Driving around on the planets for these things is maddening. They’re so far apart, barely drop what I’m looking for, and there’s never really any danger to break up the monotony.
Can I obtain these materials for engineering/synthesis from asteroids, or do those only drop the cargo space minerals used for trade?
In case of Manganese (you’ll have to do research for Phosphorus yourself), since it’s common in raw group 3, I would go rather after Ruthenium and trade down.
You are looking for
EDIT: mining will also give you raw mats but rather lower grades and I don’t know how to search for a ring so you get mats from group 3 and not another one