The damask is so elegant, that I wonder if you will really like the look of cotton fabric with the beautiful linen. Maybe if you used a washable satin or another fabric with more of an upscale look. Think Shabby Chic.
Fairy Frost is one of those fabrics with an extra sheen. I would find a store that stocks Fairy Frost and take the Damask in and see how you like it with the other fabrics. I think it might look very good.