You might try some pre-paint Krud Kutter, just to see, if in fact there is no sealer. I do use it to clean wood. You need to let it dry well after cleaning, and yes, I have used it on unsealed wood. I spray, leave it a few seconds and wipe hard with paper "shop towels". Test in an inconspicuous area to see if you get as good a result. Based on pic 2315, I suspect some kind of sealer disguised buy a build-up crud, over time. A penetrating low-sheen sealer seems a reasonable finish. It was stained once so I don't think it will eat-up quite as much stain as you think. As for sheen, it will look best with the least amount of sheen, (IMHO
). Some people do like a satin finish; I have a client that likes a satin finish on his wood paneled gazebo.