The navy is already well established in the chairs, so I wouldn't make the new rug predominantly blue. I'd look for a warm flax/tan or oatmeal ground with a little softened navy and gray in the pattern. That would connect the chairs to the silver sofas while still relating to the warm wood around the fireplace. Your current rug's quiet, varied pattern works with the room; a larger rug in that same spirit may be easier to live with than a dramatic new color.

For this main room, I'd use your concern about the wool/viscose blend as a useful filter rather than talk yourself into a rug you already worry about. Compare 100% wool options in a low or medium pile, then check each maker's care instructions and return costs for the 10x14 size. Lay the samples on the floor beside the sofa and chairs in daylight and at night, not just against the upholstery in your hand. Before ordering, tape out 10x14 to see where the chair and sofa legs land and whether the rug leaves enough wood showing around the fireplace. Of the samples you've tried, is there one whose color you liked but whose fiber or pattern ruled it out?

I'd choose something with a bit more statement value to tie in the fireplace.

https://www.perigold.com/rugs/pdp/madison-couture-rugs-tribal-elegance-bluerose-hand-knotted-wool-area-rug-p100220980.html?piid=907527142

Add a larger end table with a table lamp where the two sofas meet, or swap the navy chairs and the loveseat if you need that spot open.

Replace all the navy accents...just way too much of it. Choose a rug which works with the gray sofas, works with the two navy chairs, and invites the warm tones of the floor and fireplace trim into the mix.

https://www.perigold.com/rugs/pdp/madison-couture-rugs-wool-area-rug-p110033832.html?piid=1893700445

When you get the new rug position the furniture closer and purchase a much larger coffee table. I like this one from Wayfair because it acknowledges the stain of the floors and the fireplace.

Next time you purchase a sofa buy two; not a sofa and loveseat.

Viscose is NOT CLEANABLE. The minute water hits it, it turns brown.

I'd fix that chair you've placed in a corner to make it a more desirable location for reading.

The dark navy blue pillows could remain as a backdrop for patterned pillows.

warm up the reading corner with a bamboo blind on the windows.

If you dont want to get rid of your armchairs ( they are a beautiful dark navy) you can play around with them by adding more navy / blue accents but in small doses.

Your curtains are fine but adding valances / roman shades underneath in a greek key trim in navy blue will tie well with the armchairs .

Right now you have blue on blue in your pillow and armchairs. Swap the armchairs pillows for a sheen or metallic ivory/cream. And rinse and repeat again with the silver sofa by using dark navy pillows in a pattern so the blue goes easy on the eyes.

For your rug, finding 100% wool rug your best bet would be traditional Persian rugs but if you cant afford the price tag of Persian Rugs, something softer in a blue would work. The key is to find a blend of blue and white.

I wouldn't recommend a solid light rug because your whole room is light and bright while your chairs are dark and so is your mantle/fp. Even a light rug with a little pattern or lines is better.

But a rug like this would work well. This is from Surya 10x14 and I believe wool. It is similar in style to your previous rug but has light blues mixed with the tan/beige so your entire room is blended well.

Regardless, your best bet is to add touches of that navy or baby blue or for more of an accent a burgundy/red or terracotta yellow to pair with the fireplace.

An accent pillow such as this could also work behind navy pillows on the sofa only. These 2 rugs could also work while they are less patterned they still have a little trim or border to go with the theme.

Very helpful advice thank you for all of these suggestions. I appreciate it!

Try the Heriz rug. It’s dark but your space could handle it the colors are divine ://www.roomandboard.com/catalog/rugs/patterned-rugs/heriz-rugs/625136?cam

https://rnb.scene7.com/is/image/roomandboard/044904?$thumbnail$&size=256,256&scl=1