Solid Hardwood, Engineered and Laminate Flooring - Strip flooring on stairs

I want to put 2-1/4 strip flooring on my currently carpeted stairs. I think I have figured out most of the details except one-

How to get a tight fit to the riser? I asked this before and someone said to scribe it but scribing is not possible on the piece placed last against the riser.

Since my risers will be painted white, I'm thinking of taking the easy way out and getting a close but not perfect fit to the riser and then gluing a 1/4 plywood face to the riser to cover any gap and/or nails on the existing plywood riser.

Am I making sense?

Thanks

I have read posts on this forum where installers tend to report that installing strip flooring on stairs tends to look "cheesy." I sell hardwood flooring and stairnoses to folks who do this very thing. The stairnose is what caps the front edge of the riser and cups down and over the riser to hide the gap. There are dealers who sell treads and risers, which are solid pieces of wood made especially for stairs.