Sorry, I don't have an answer to your question about a fabric company that matches fabric.
I do have a few suggestions for you to consider:
You can contact Spoonflower to see if they would be able to make fabric to match your color from a scrap. I know they make custom fabrics.
Don't forget that you can use the back side (wrong side) of some fabrics to see if the color matches.
Lastly, I have a friend that dyes fabric when she can't find what she wants in the store. She has gotten spot on to matching one fabric she ran out of. Best of luck to you!