I find red oak to have a pink/cinnamon cast to it...whereas the maple/hickory are MUCH MORE gold. I foresee a clash of undertones with the red oak. Of course, if you PAINT THEM your fine. But a natural (even a stained finish) with red oak is going to cast a different colour of wood. The maple cabs, though a pale fleshy colour right now, WILL turn to a slightly darker GOLD. In a year or so, the cabs should be a very close gold/yellow match to the gold in the hickory (which is why I like the two woods put together). The red oak, will start out a pinky fleshy reddish hue...and stay that way. It will clash until you stain them or paint them. Your current front doors are OK-ish. The brown is just about right for the hickory. A snick on the reddish side but nothing I would lose sleep over. That's as "reddish" as you want to go with hickory. Red Oak will be worse until you paint.

you are just going to have to get samples and try them out. have no idea what your room looks like or the type of light you get. what you don't want are cool gray colors. red oak is warm,,,you need a warmer gray, or a neutral gray. (BTW,,,I have Silver Half Dollar on my walls and it looks like a baby blue. I get afternoon sun in the room and they are tall ceilings. It's very blue once up. I have it paired w/Kendall Charcoal and silver travertine, so it still works. but w/a red oak floor, I'm thinking you won't like it) Get some samples! some of the colors you picked are on this,,,next to a cool, blue/gray tile floor. to me, these two tones clash. you may like it.

@Amy Molina thank you for advising. your color really is beautiful!!! i just selected last monday chestnut/classic. it did not appear to have any of that red orange showing through - just a nice neutral brown color. in my opinion, it is like a special walnut but greatly improved. special walnut was a yuck! color on my floor showing orange and the grains too bold. classic gray is the ticket to modernize a color if looking for a brown. its just finding the right brown that is tricky. now i am just hoping i selected a dark enough brown - yoir looks great! they come and do ours tomorrow in the official color.

I am wrestling something similar except I have hard wood I am staining and adding new to hall way. I feel like I need to use golden oak (my guy uses duraseal). But I was thinking of going a little more brown. Please let us know what you decide. I might check out nutmeg for my red oak flooring. Suggestions...I will let you know what it ends up or me