Here's my somewhat limited experience with cloth sails, and trying to model with original materials in general.
It can be successful only if you overcome the scale problem. Without too much research into cloth thickness, imagine a piece of typing paper is about 0.004 inches. multiply that by 350 and it would be 1.4 inches thick. So a piece of cloth, which would not be much thinner than paper and still be practical to cut and shape, from which a little sail is made, is a pretty thick slab. It wouldn't be able to have realistic shape.
Real sails have reef points and reinforcing, plus hemmed edges and a sometimes built in billow. Any of that cannot be replicated in such a small scale, and only in large scales with a lot of craftsmanship.
I did not understand the weight of sail issue, it seemed to me that tension in the rigging would be a bigger issue, but it's true that plastic yards have no stiffness at all, compared to wood. Another example of scaling.
I'm impressed if you took that on, but.. I made a cloth sail for a 1/50 scale Dhow, a single piece about 12" on a side triangle, and I worked at it for a month. And the bigger the easier to be accurate.
Try doing one, if she has a fore/aft sail. I'm guessing the square sails are about 1" tall by 3" wide, which is a little slip of a thing.
Furled sails are easier by far, and bare poles are a good look too. But don't discard those vacform sails, if you don't want them someone else will, because the old ones fall apart.
Bill