Lean into a moody color that blends in the unfortunate floor. Consider one you have sampled that I marked with a red star below. You are really on to something going that moody direction.

Drench the walls, trim, stairs, and ceiling in the this color. (The question is always where to stop as it goes up to the second floor.)

With white paint the sad tile floor pop just as much as the banister so you are not really left with any historic vibe at all - the banister just doesn't stand out. With the darker moodier color, the floors would blend in more and the banister would be what your eye is drawn to. It is really beautiful and such a nice feature of your home.

Also get a long runner to put here so you see as little of the tile as possible. Get a dark muddy color runner so the tiles don't pop from behind the perimeter. And get a new light fixture. The pattern this one throws is dizzying.

I don't know if Farrow and Ball is in your price range but their Dead Flat paint is really easy to clean so is great for narrow hallways that get scuffed easily. Their color Elephant's Breath comes to mind. Here are some other brands that are sort of similar in color, though the color you tested already might work just as well.

https://www.matchmypaintcolor.com/farrow-ball/elephants-breath-229#google_vignette

I hope you post an after pic. I'd love to see how this turns out. I owned a home built in 1852. I found all kinds of ways to honor the historic parts that were still left while blending in the new. The trick is to make it not look faux old-timey.