We're renovating our house and refinishing the main stairs (this is a multi-family brownstone). We're removing linoleum tiles and metal nosings, and we'd like to provide a smooth, durable painted finish to the wood below. I'm trying to avoid too much scraping or sanding of the wood because of lead paint.

Is there a self-leveling floor paint that I could apply over the wood treads that would take out some of the roughness? I was thinking an epoxy product, but most are for use on concrete floors.