Prof.
I sure have tried to find this nylon you speak of, but it doesnt look like ive had any luck!
Last weekend, i went around rubber clark stores near me and i have been guided to of total 3 types of nylons that are white, all three of them dont seem suitable to me, so i did not bother getting samples.
I have taken pictures of the ones i was shown with my phone, so dont expect much of quality, but might give you an idea and see if any of these are what you have, and ill try to explain it as best as i can

First one is a hospital film pvc white.
It is a nice material to the touch, fairly white and sturdy, pretty thin but didnt seem transperant like you mentioned of the one you speak of.
The problem with this material is, it has lines throughout it, more so like zig zag lines, imagine someone with a sewing machine did some artwork on it every 3" alone the way going zig zags and sideways... so i dont see it being this.
Sorry the picture didnt capture the zigzag lines as they were very fine and same colour as material and i dont think my mobile was able to capture these lines.
You wouldnt see these zig zags from say the seating position, or even 2 meters away most likely, and i dont think teh picture would be so badly afected, but just the thought of having these zig zag lines would make me stare at the screen trying to look for them, plus its just not right to have these lines for a screen!
If it wasnt for this zig zag pattern, this would be a very good candidate.
Its also the cheapest of all.


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Next is this material called ripstop nylon.
Defenatly not my liking, was very see through material, meaning very thin, if you put your hand behind this material, you could see your hand through it!
Also, it had squares on it. imagine a pattern of a VGA pixels that seemed like printed on.


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And finally, another pvc reinforced backing nylon.
Nice and white, one side had a shine, teh other a matt finish look to it, teh problem! well, it also has a pattern on it(why cant they just have a plain white nylon with no surface pattern???).
Just the same as the previous one, but this pattern looked more like pixels of say a svga, but not printed on or anything, just like made as such when processing the material, like a part of the material, where it was specifically stretched as such.
It felt like a rubberised material too, and not cheap, $35/m.
As with teh first one, very good candidate if it wasnt for the pixel surface, and its very think, no backing would be required for this one as it already has a backed material.
It also comes over 2m wide, shame really.


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So yeah, this is what i have found so far, and will still have a look every now and again when i come across some stores on my ways, but even then, looking at the materials, it seems it would be much harder to stretch them perfectly, would be harder to clean(the ones in teh stores were heaps dirty from finger marks/handling etc), as you cant press to hard without leaving dents/stretch marks and weather affected as you mentioned.. so for now, this melamine board is looking very promising as you have just experianced.
Glad you could have tried it out yourself and thanks for your feedback on it, yes it does seem to me that its one of the easiest/cheapest and a very good performer if this is the kinda way people want to go about it.
cheers,
Danny