Such a nice space! All that wood is going to boss around your decorating. You are smart to try to work with it instead of fight it with cool colors. I think orange is definitely out as an accent color. It is just going to enhance the orange tones of the wood. I would consider painting all the doors in the dining space, it will make the space look less chopped up. I saw on another thread that you are replacing the kitchen floor. Have you considered a slate look tile with faint brown accents? Your floor will have a nice clean look and the accents will work with the wood and will look good with your taupe cabinets. Daltile porcelain slate.

I second Uptown's Post as I just installed Mirage floors throughout my condo. If your budget is really $4 to $6 for wood floors, I think you need to realistically evaluate your budget because wood floors in the $5 range will not be high quality flooring. My Mirage floors are engineered and probably what would be considered moderate quality. They were about $8.00 per square foot without installation and with the very complex installation I had, the final cost with materials for installation plus labor was about $18 per square foot. I went with their red oak natural Select & Better because I wanted a light floor that wasn't the star of my design. It's not trendy and I know I won't tire of it because it's essentially the same floors I've had all my life :-). My floors really look very pale blonde. I had considered white oak but I have a lot of Quarter Sawn White oak - kitchen cabinets; wall units for den/office plus a custom wall unit in my dining area and I wanted the floors to be more of a contrast. I am delighted with the result and everyone who has. seen it loves how it contrasts with the other woodwork and makes my whole place look open and airy. ETA - And if you are purchasing floors directly, you really need to check pricing at different vendors. Even if you are purchasing through a designer, it's a good idea. When I called dealers, their prices ranged between $7.50 and $9.00 per square foot. My designer purchased the floors and obviously got a discount and then I paid for them plus her markup; sales tax so my final cost for the flooring was about $8.00 per square foot.

I recomend this conpany for very high end commercial grade porcelian tile. We replaced all our high end real wood with their tile and we LOVE it. Very low maintance and no requirements for special cleaners. They have tons of options for wood grains and colors. We have had the tile in our bedroom for over five years and it looks as nice as the day it was put in. We just finished redoing the rest of the upstairs in the same tile and are thrilled with the look and the quality. https://www.bedrosians.com/en/product/detail/titus-tile/?itemNo=TCRWT Here is another color option:

Lovely floor. You want to do white on the walls to go with it and the gray sofa. That’s all and good, except for one caveat….the natural light will really impact any white you choose. North light or East light: try B.M. Goldtone. South light : try B.M Gray Owl. West light: try B.M. Patriotic White. Those are my recommendations, but I think you should take a minute or two and read this great article from Domaine, where B.M. pros answer the question of which white to use for walls. https://www.mydomaine.com/benjamin-moore-paint-questions