You may want to consider using system text for such indications rather than rehearsal marks, either completely instead of or in addition to. Rehearsal marks are centered on their barline, whereas system text is left-aligned with their start position - this might produce less ambiguity as to where the named sections start from.
Dorico does a lot of collision avoidance automatically, but I think it’s fair to say there’s still fairly often some need for considered input with an engraver’s hat on - here, that might include inserting a system break at bar 68 or 69 to allow more horizontal space for the 2 preceding section indications.
(For your info also, part of the reason I couldn’t quite picture what you were describing based on your initial post was that in Dorico, this is what comments are - obviously no one expects everyone to pick up the Dorico lingo completely and immediately, but that’s one reason why it’s recommended to include a picture or a project as part of posts, or a bit more detail about how you’ve reached the point you’re at if possible, e.g. “rehearsal marks with extra text included as part of them”)