Can you define more precisely what you want for output?
All four screenshots show mesh models, which are useful in many scenarios but not all. You reference "clean geometry for export" Do you mean non-triangulated geometry? If so, then the answer is Yes, the Revit API exposes non-mesh ACIS solids for most native building element geometry.
Before you go too far, try this:
Export DWG -> settings -> Solids -> "ACIS Solids"
This should give you not the "long faceted polys" but actual curved surfaces. If you are still seeing them as faceted in other software, even with this setting, it is probably due to the other software. This is a good reference for how Revit stores the geometry internally.
HTH!