I've done quite a few synthetic head djembes.
I use the Remo NuSkyn heads that come preformed in 13" (with the flesh ring already in it). I have to find a shell that fits the head. I've contacted Remo and Toca about being able to get sheets of their material so I can fit it to drums a little better, but they both say they don't sell it. I haven't looking into other materials. I have used the fiberskyn heads as they look better (at least more natural).. but they sound too plastic. They have 13" and 14" heads for djembe, I've never tried the 14". They have this skin for other drums, bongos and congas that is a thicker mil, but available in more sizes under 13". I've used the NuSkyn "tucked" and the "weatherking" same material but the tucked looks more natural.
http://remo.com/portal/products/3/12/116/263/specs.htmlThey don't stretch at all and I have never broken one. I've put some crazy amount of tension on one to see where it's breaking point is.. just never did break but did start sounding like a doumbek.. so maybe was thinning out?? not sure. They sound their best cranked up as solo drums, as the tones aren't so hot with the thinner material, and with the bearing edge a little flat on top it helps mute some of the overtones.
I don't think you can buy direct from remo if you want to go that route, but I bring in a few synthetics every so often and can get one to you...
On another note... I work with some banner material as well at a sign shop, it's no rip material with fiber inside. I'm not sure if it stretches or would hold up to drum tension, but I eyeball that stuff all the time wondering... I'm guessing it probably stretches though.