Personally, don't like the Olympic paints or the Gliddens. If you're limited to Home Depot, I'd stick with Behr PremiumPlus.
Anyway, I'm not finding either color you mentioned except in different paint brands and those colors are QUITE dark. My thought is, if you're looking for something different to what you have now and are looking at such dark colors, then I'd continue the red into the FR. However, then I looked at your fireplace and thought, no.
Also another thought is that the chairrail on those two short walls is contributing nothing to the coherency of the room. Think it should go.
Okay, back to the beige/tan furniture and the very tan/orange fireplace. And the tan floor. sigh. I'm going to have to go off and work on this one a while. It sounds like you're heading in a green direction? So when stumped by a combination, I usually trot off to THIS website and look at their fabric moodboards which can really help to unite a space. Like this one:
Vintage tan and redYou need some fabrics to unite this space and help it work better with the kitchen. These stripes and some of the florals have the colors that could help bring everything together. Then pull your wall color out of the fabric. Don't make it the strongest color -- choose one of the more subtle colors and go with it. For instance, I'm seeing some khakis and light neutral sages here. Something like Behr's Expedition Khaki 340F-4, Bavarian Cream 340E-3, or, lighter still, Cottonseed 340E-2 which aren't too far off from what you have now but more in keeping with an overall coherent room.
A more green color would be Ryegrass 390F-5 or the lighter colors on that strip, including Rainforest Dew. However, I like the khakis better with your fireplace.
But really, you need something to pull all the colors together first. Otherwise, your current wall color doesn't look too bad.