If I recall correctly, your companionway steps look a lot like mine.
I used a polyurethane semi-gloss finish with a UV inhibitor. Specifically, Minwax Spar Urethane. Unfortunately, I can only get the water-based stuff locally now due to Air Quality Management District's regulation and it is not as durable.
Anyhow, the stuff is tough and easy to apply I get (got) about a year between coatings, and that's with heavy use. (Now six months with the water-based stuff.) Scuff it down with a 3-m pad or light sanding with 150 grit and vacuum or brush out all the debris from the grooves. I use several sizes of foam brush to apply. Between coatings, I clean it with a wood floor cleaner and keep it clean with a vacuum.