Na. Yes I've experimented with just about every type of plastic you can imagine. (projector sheets, colored vellum w/plastic laminate, Grafix craft plastic,static cling film) All of which work well to some degree. For instance both the vellum w/laminate and projector sheets work well on smaller figures. However, on larger figures it tends to be a bit floppy. Light transmission is better when color is placed directly on the plastic. The Grafix static cling film is great for scenery if your using a glass panel in front of your screen and you don't need to change scenes.
I wound up using the .08 clear plastic sheets because it was available in larger sizes. Not sure how well it will work when I actually try fitting the moving parts together. Like I mentioned before, I'm using glass on the backside of the play area to give support and a smooth surface for the plastic to glide across. (If you use plexiglass it will scratch and the scratches show through.)
I'm trying really hard to find the right material to simulate the traditional animal skin effect. I have one more method I want to try. I'm going to stretch linen over a frame and color it with ink. Then put a heavy starch coating on it to stiffen it. If all else fails I may just have to kill a goat and start tanning the dang hide!
It sounds like you have two separate issues:
1. A plastic that is capable of taking ink
2. A plastic that isn't floppy
It may be better to ignore #2 - that is, find a plastic that's suitable for drawing, then worry about holding it up. This, I've found, is more about rod placement and gravity than the type of material you use. So long as it doesn't break, the plastic will be problematic at larger sizes no matter what you use. If your screen is slightly tilted towards the audience, some of the 'floppiness' is avoided as your materials will work with gravity and pull down towards the screen.
As for #1, I'm afraid I can't help you there. The only thing I've ever tried is watercolours on the thinnest white cardboard I could find. Maybe instead of finding a substitute for animal skin, you find the best material for drawing on and then 'fake' the skin texture .... like how you can make a piece of paper look old for pirate treasure maps....
I like the idea of parchment too - I've actually just been looking at things to stiffen paper with, because that's what I'll be using for my super secret project. Paper is incredibly flimsy, but it's the only way to get my effect to work... Perhaps parchment with a fabric stiffener might work?