Remove the teak steps and replace with Trex. No more maintenance issues - just power wash (hit them when they're doing the bottom) occasionally and forget about them. I've done this with a LOT of my exterior teak, and have no desire to go back to teak. Just about the only things still teak are the toe rails. Took a piece of the trex to Benjamin Moore and had them match up a can of satin enamel - toe rails are now painted to match the trex. Looks fine to me and the Admiral.
If you've really got to have gloss varnish on the teak, go for it. But teak is a poor wood to try to varnish to start with - it's too oily for the varnish to hold well. Even the BM paint doesn't hold well - starts to peel here and there after a couple of years. I just scuff up with 80 grit and give another coat - good for a while longer. My only remaining topside varnish is stuff I bring home over the winter and refinish - tiller, lazarette hatches, drop slides, etc. Lazarette hatches are teak, but are sealed with epoxy then varnished. Even so I get some spots that are troublesome and need more than just sanding and revarnishing.