Hi there - with the amber wood vertical beams I agree that a warm neutral is going to be a good fit for your room - better than a green-gray. With the skylights and the vertical orientation of the beams, you have an interesting challenge - if the beams are amber toned as you mention, you might test sw crewel tan or sw softer tan http://www.sherwin-williams.com/homeowners/color/find-and-explore-colors/paint-colors-by-family/SW0011-crewel-tan/ I particularly like moderate white (the lightest shade on the softer tan card) since it has the right undertone to work with the amber wood and black - http://www.sherwin-williams.com/homeowners/color/find-and-explore-colors/paint-colors-by-family/SW6140-moderate-white/

You might start with moderate white on the walls and ceiling in the main space and move to the tan as accent walls or interior walls of rooms you want to give a more cozy feel. You can often treat interior walls as a box within a box in a modern home if you use the paint strategically. This is an architecturally modern home and the simpler off-whites can lend a real museum quality / architectural feel, particularly when natural wood is involved, and it may lend itself more to accent walls than most styles.

You may or may not have wood trim around your interior lights - I have seen some bamboo flooring used as trim on interior openings that was particularly lovely here on this ideabook that reminded me of your place due to the tall narrow openings https://www.houzz.com/magazine/houzz-tour-a-san-diego-townhouse-gets-a-bright-update-stsetivw-vs~9041804

If you want green integrated I would suggest some of the earthier greens - a palette of moderate white, crewel tan would be super with ruskin room green http://www.sherwin-williams.com/homeowners/color/find-and-explore-colors/paint-colors-by-family/SW0042-ruskin-room-green/ and accents of chinese red to warm the room up. http://www.sherwin-williams.com/homeowners/color/find-and-explore-colors/paint-colors-by-family/SW0057-chinese-red/ You might use a dark red-orange like sw fireweed to paint a hand me down piece of wood furniture. Or use the green in a kitchen to add warmth and charm. I've seen some terrific neutral green upholstery that is practical and also is really versatile in this sort of olive tone to work in nearly any color palette.

Sage green.

I really love Benjamin Moore Sag Harbor Gray. It is grey with a lot of green and looks incredible on the walls and quite different from the paint chip. It is beautiful in bright light or at night and changes with the environment in a serene and sophisticated way. Perhaps SW can match it?

Offwhite walls.

Use sage/olive for painted furniture/sofa. Combine with more wood, wool, leather, stone&charcoal grey, some (sea) blue.

If you desire a modern feel, stick with lighter neutrals on the walls, using color in artwork, furniture, and accessories. Don't compete with the wood tones by using greens or golds. Be aware that walls too white can feel stark and any other neutrals used such as duvet covers, towels, etc., may not go with. I would suggest you find a medium, neutral white, cream, or "greige" tone in something you plan to decorate with so the potential for conflict is reduced. Beautiful setting!