That sure is a lot of wood. It is beautiful though. The current floor looks a bit off, so I can imagine you want to change it.
A matching old pine floor would be lovely. Or a light slate(-look) tile. Or a solid smooth floor in concrete, linoleum or epoxy. I would be careful with darker warm colors, so personally I wouldn't pick walnut. Only a charcoal/black stain, but that most likely will be too dark. Maybe chalk stained oak (pale grey-white-wash, like the bleak look of the treads).
I do like the look of the floor going into the kitchen, but if a pine floor would not work with the maple cabinets, consider a stone floor in the kitchen, it will look ok, because of the fireplace (copy).

The slate (or a grey ceramic wood!), concrete, linoleum or epoxy would probably be my pick. Floor heating if possible. A nice wool rug.. But then again, a chocolate stained floor with all that wood can look good, if you can accept it's darkness.

reqreation...How about this one? (See below)

Love it! I'd suggest oil instead of varnish. Use white oil to keep the chalky pale grain.

Ok I'm going with this one! I could not find anything that calmed all that wood down but I think this one does it.

Great choice! I think it is going to turn out perfect.