I am biased because my exterior is Diverse Beige. I looked at Accessible and I thought I saw some green in it. I would choose Diverse for sure. I think of the two whites you mention Divine is best.

Accessible Beige in my whole house. All of my cabinets, built ins, and trim are BM White Dove. I like it a lot. looks nice together.

Painting on the walls will be hard to cover up. Sampling color on the color you're trying to cover doesn't give it realism The samples are too small. Get bigger samples (paint cheap framed canvas from Michaels) and test them on all the walls throughout the house (being on canvas makes them easier to move. Purchase Samplize ($6/each) and use painter's tape to move them around. It took me 6-mos or more to test samples. If you don't/won't limit your time then Accessible Beige will be the easiest to blend. The floor is brutal and if you go lighter, it will go darker.

You have to think about neutrals like the color wheel. You have pink beige, orange beige, yellow/gold beige, green beige, greige (that color between green beige and green gray that sometimes looks gray sometimes beige), green gray, blue gray, violet gray and taupe ( the color opposite of greige, somewhere between violet gray and pink beige. Accessible beige is very popular because it works well with a lot of colors, but that doesn't mean it is the best beige, it just means that it is safe. I don't like to start my color journey with the neutrals, but you kind of already started the journey when you selected your flooring, so it complicates things a bit. If starting from scratch, I like to start with the colors (not neutrals) that make your heart sing. You already mentioned sage green and burgundy. Honestly, with a true burgundy I like a bluer green than sage and would pick something a bit more orange with sage. Blue green with burgundy vs blue green with the more orange tone in Sun Dried Tomatoes Sage green with Sun Dried Tomatoes Sage with a true burgundy With a sage green and a deep red like Sun Dried Tomato I like both Accessible Beige and for a bit cleaner look I like them with a color similar to Creamy. With a blue green and more purple burgundy the Accessible Beige feels a bit muddy and Creamy feels too yellow. I would lean more toward the grayer taupe colors. The sage and sundried tomato doesn't feel right with the more taupe wall color. Your challenge is to find the neutral that works with the colors you love and with your flooring. The paint stores give the little cards away for free. Pick up 5-6 dozen sample cards and take them home. Pick up neutrals and the colors you love that you will want to buy when you look for bedding and art and area rugs and whites. Take a sample of your flooring outside and look at the swatches in natural daylight. Some are going to look pink and some are going to look yellow and some gray and some green . . . Only look at one or two colors at a time with your flooring so you are comparing them to the flooring and not to each other. Once you have narrowed your choices down to a few that you like mix in some of the colors you love and narrow your choices to those that like with your flooring and work well with the colors you love. When you are down to 5 or 6 choices order larger swatches from Samplize.com or get sample jugs and paint your own samples. Do the same thing with the larger samples. Look at one at a time. It is best if you have someone helping you who can change the swatches and ask which you like better "A or B" without telling you the color names. We sometimes like or dislike the name and our mind tricks us into wanting to like the color. Here is a picture I took while sampling colors with my flooring, furniture, bathroom tile, bedding, bath towel . . .