I like the Japanese Maple miniature as it wont grow but will add a nice reddish maple color.

Texas has a hue amount of opportunity. 

I am thankful I own properties in a reddish state like FL and would only purchase a property with similar states that are at least somewhat landlord friendly.

You've got a lot of red/orange in your existing floor; tone your other levels towards the reddish-brown spectrum, and pick up the gray in your carpet runner (which you should definitely plan on using as stairs without carpeting/runners can be slick whether wood, laminate or vinyl). 

New spring leaves emerge a reddish bronze color, maturing to a glossy green.

I had modest success by wiping on and then wiping off some cherry-colored wood stain on a reddish floor.

It's not completely white but goes well with the reddish tinge that cedar has.  

The main color should be in the middle hue range, then one accent should be darker and one lighter.

@Kevin ReaLived:Lagos Nigeria 🇳🇬 Dublin Ireland 🇮🇪 Cork Ireland 🇮🇪 Dundalk Ireland 🇮🇪 London England 🏴󠁧󠁢󠁥󠁮󠁧󠁿 Cleveland OH 🇺🇸 Saint Johns FL 🇺🇸 Savannah GA 🇺🇸 Charleston SC 🇺🇸 Columbia SC 🇺🇸 Multiple visits:Singapore 🇸🇬 Hong Kong 🇭🇰 Hue Vietnam 🇻🇳 Lithuania 🇱🇹 Estonia 🇪🇪 Greece 🇬🇷 Copenhagen 🇩🇰 Malmo 🇸🇪 Stockholm 🇸🇪 Helsinki 🇫🇮 Saint Petersburg 🇷🇺 Sanya 🇨🇳 Sydney 🇦🇺 Brisbane 🇦🇺 Melbourne 🇦🇺 Tasmania 🇦🇺 Wellington 🇳🇿 Auckland 🇳🇿 Christchurch 🇳🇿 Southern Italy 🇮🇹 Nice/Monaco 🇫🇷 Berlin 🇩🇪 Playa Del Carmen 🇲🇽 35 of the 50 states 🇺🇸 (Includes Hawaii)*make no mistake whatsoever:ABSOLUTELY NOWHERE COMPARES TO NEW ZEALAND.I would relocate right now.

neutral and lighter in hue.