I like Sherwin Williams Wood Classic varnish. Any oil based finish adds the amber tint. I generally use Minwax, HD or Lowe's. You will see an immediate change. Hand sand with 150 grit paper. There may be problems after applying the new poly---because of the number of coats on the stairs now---bubbling, checking, that sort of thing. I have used oil based over water based successfully in the past---but not over 10 coats. If you have to remove the water based, stripping will be much faster than sanding---poly clogs sandpaper quickly.

Don't try to mix & match floor stain; whatever you have on your hardwood floors is what you should have on your stair treads. If you really like the darker stain, you could always have your natural oak floors refinished.

Beth H. : - thanks so much for sharing those last two images. I'm working on a staircase in an addition to our old house and I've been using Houzz images to help the staircase maker understand what I'm seeking and hadn't seen those. And I agree, Houzz has chronic "control issues" when it comes to sharing images easily from other sites. I really think the owners have ambitions to take over from Pinterest, Instagram, Facebook and Twitter, let alone all the also-rans, ugh. It's a sharing world, Houzz - get with the program! Anyway, about those images you've shared; are they from Houzz? I tried clicking on them to see if they'd open a post, to no avail. Thanks!

Darker is BETTER. Like in sewing seams on a garment, it is better to do DARKER with the tread than it is lighter. Jacobean stain has been used successfully to remove the red from red oak. If don't properly, the Jacobean stain (like water popped treads) will come VERY close to the tone/colour or the DARKER stripe in the feature wall. To keep the country theme, you can have the RISERS painted WHITE. The WHITE will help the Jacobean 'pull off' this change. A small bit of separation from the floor colour, the tread colour and the feature wall colour is all that is needed to FOOL the eye into thinking everything is tone on tone on tone. Water pop + Jacobean stain + ONE COAT of finish. Remember: the FINISH is what will add more yellow/orange (oil based or oil modified poly) or NOT (water based poly....like Bona Mega One or Traffic or Traffic HD). Find out the FINISH for the treads. You will be picking blind if you do not have a coat of finish over the stain.