I have never used a turkish towel, and am having a difficult time envisioning how you would wear a towel with a scarf or shawl? Do you mean to wear it as a coverup wrap when you go swimming?
Also, why linen specifically? Linen does dry quickly, but are there other qualities about it that you're attracted to?
If you're willing to sew, a towel wouldn't be too difficult. The hardest part is sourcing the fabric. JoAnns and similar stores don't have great selections. I have a few fabric swatch books for fabric suppliers, but most of the swatches I have are for cottons and silks. I can look around though.
Right now, I use a Packtowl for the gym and for traveling. They seem to serve their purpose so I haven't given much thought to towels. A nicer towel could convince me to switch though.