I do alot of applique and have always found muslin too thin for background.
If I want a antique look, I use Kona white cotton & dye it. Rit dye has a tea stain color, I wash the cotton and dye 1 shade darker than the color I am looking for and then wash it again to remove any excess dye. Then dry & press, using spray starch. Ready to go! Kona cotton is tightly woven and rarely is there a show through.
I also cut my background atleast 1 inch bigger than required, leaving enough room to resize the block to the desired size. Hand stitching distorts the fabric quite a bit and I want enough of a fudge factor to make sure I can size up correctly.