If you have already made the sails, you're starch idea will probably work with a little experimenting. Or you can look for a product in sewing supply stores called sizing. It's used to produce stiffness and fullness in necktie backing and such.
A friend has a 36" model of the Donald McKay designed and built Flying Cloud... a three masted clipper from about 1851. The modeler used a good grade of calligraphy paper. The nice thing about the paper is that it can be purchased in differing shades of color... from a slightly tea stained look to a bleached cotton sail look. To make the sails appear full with this material, he simply rolled the model sail around a pencil to achieve the full windblown look. A little artful wrinkling produces a sail that appears quite realistic. One problem encountered with cloth is that the weave, no matter how fine, didn't look to scale... Best of luck!