You are fundamentally trying to do the wrong thing.
Normally PCBs are intended to be functional. Most quality manufacturers will make them according to
particularly relevant IPC standards and according to their own quality & capabilities policies.
For the most part minor cosmetic defects that are aesthetic and not related somehow to PCB reliability / quality aren't even specified in the relevant specifications & standards as being prohibited.
Then expecting "very low cost" PCB suppliers to make PCBs that are basically cosmetically perfect as well as functional for nearly no profit is not reasonable.
You are onto something, though, in that more and more PCBs are used not just for enclosed "out of sight" boards, but are used in user visible places like keypads / input devices, displays, front / side / connector entry panels, lighting displays, art projects, etc.
So for those reasons more places probably should offer some kind of better finish options for ordering, and more materials and treatment / production options accordingly.
Anyway other than saying "don't expect that" I have one idea to offer -- perhaps you could try one some kinds of self applied refinishing / finishing treatments to the "visually imperfect" PCBAs --
* rubbing / buffing / polishing / sanding / ...
* coating (wax, polish, clear coat, gel coat, dye, paint, dip, ....)
* hot air, baking, soaking, ...
I mean look at all the old weathered / damaged "antique" or "worn" plastic, wood, metal, composite kinds of items
of all kinds that people can easily restore / refinish to beautiful sparkling condition often with just a little bit of polishing, buffing or similar fast / cheap techniques to improve the surface texture / coating wrt. abrasions or defects etc.
You're having 99.5% of the work done for you making the PCBs for essentially "free" so it seems like it might be
worthwhile to invest a few minutes into a little cosmetic finishing / touch ups if the appearance is so critical for your "art project".
Otherwise maybe some kind of cover layer labels, decals, film / artwork overlay which can be made visually perfect can cover the majority of the PCB surface so the finish of the soldermask and fiberglass is not such a big deal for you.
After all they make boats and cars and what not out of the same kinds of fiberglass processes. Underneath it isn't pretty but they put a pretty surface layer / coat on it over the structural interior.