Looking for ideas please on the best way to complete this trim. Do I run the 1/4 round to the floor and trim the baseboard to fit, or run the baseboard to the stairs and [somehow] match the 1/4 round to baseboard? Or other options>?
Fill the gap with a plug at the space between the stair stringer and wall (2nd photo: where the floor molding disappears). Or cap the beveled end of the stair stringer with 3/4" pine with the stringers profile.
If that gap is closed the floor molding will butt against it. Than the quarter round can be terminated with a face bevel right equal with the stringer.
The gap has to be covered in order to have an flat (90 degree) surface to cut the molding's to.