Furniture, Wood and Cabinetry Finishing - 82 year old wood staircase

I have just purchased a home originally built by a carpenter that has a gorgeous 82-year-old wood, curving staircase, which I believe is red oak or cherry (the raw wood visible where a small piece broke off a riser has a medium brownish-red tone like the color of unfinished rough cedar). The couple who sold the house to me added a side to the staircase at the bottom where a wall was removed. The addition is a perfect architecural match, but is built out of a different type of wood. To make the sides match, they painted the entire staircase with what appears to be an opaque stain or paint (very little wood grain shows through). Trouble is that the color is a muted dark brown and is visually adjacent to dark cherry kitchen cabinets. Any suggestions on stripping, sanding, and what to use to restain/repaint so that the two sides match and match the kitchen cabinets (more or less)? Advice on a good stripper is very much needed because sanding all the square rungs spaced only one inch apart will be next to impossible.

Thanks for any help!