I can only comment about the cowhide rug idea as that's my area of expertise. Cowhide are still going very strong as a design trend, they haven't been overdone in my opinion. Also cowhide rugs break all the normal rules of standard rugs because they are an organic shape. So they visually take up more room than they physically occupy. So you don't need a cowhide rug to be as large as a wool rug. They also look better on a 45 degree angle to furniture and it is OK for one or several legs to go underneath furniture as this can anchor a group of furniture. For how to clean a cowhide rug there is some great info on my website plus a video that is really interesting.

Try a mid-century modern rug like Hemphill's Rex Ray Area Rug Collection or Jaipur Traverse Caracas. I looked up 'mid-century modern rug' and chanced upon these on Houzz. I like the muted colours which would soften the cream on brown. The mid-century motifs would highlight the mid-century chair. Good luck!

I can really recommend the Danish brand "Rug Solid, which have rugs made totally out of recycled materials. This is a photo from our living room, where we have a recycled cotton rug from "Rug Solid". http://rugsolid.dk/en/

We will be facing this dilemma in a few months time - thanks for the timely advice!