If you were my client, say a corporate portrait gig - and you gave me the Avadon look as a style source, and a sheet of your paper as a backdrop example (approaching this as if it were a job)… hmm, what the hell would I do??
If there were no budget for a set builder or stylist, I'd probably start with something like a really light muslin as wide as can be found (you can order it pretty wide without a seam, often as an existing rod-pocket backdrop). I'd figure out the minimum size I'd need - 9' could be overkill, 6' might do it? Then see how close it could be faked. Maybe stretch it out tight and use a roller to do, I dunno - clear acrylic? Which would give it some translucency (maybe) and also let you get it partially dry, then scrunch it up a bit so it dried holding some texture (maybe)? (I've had painted muslin backdrops and wanted a wrinkled look, I just used a ton of spray starch and a hair dryer.)
Perhaps while the paint was wet, I'd ID some sort of fibers or straw or… something to scatter into the wet paint...
I'd probably test on something like 3' squares - often the testing process will lead you to evolve your ideas, learn as you go, etc. I'd then have those test pieces to run by the client for feedback, an OK, or a "if I combine this coating with these fibers, I think we'll be close"… etc.
There's likely a way to get the same feel - I've seen set-stylists come up with some amazing solutions over the years. Sometimes, when trying to match some background idea, just the process of trying to fake it leads me to something not exactly what I wanted but cool as heck.
Probably not going to find a 6' roll of rice paper… though here in Dallas, we used to have a hand made paper store ("Paper Routes") which was packed with every jewelry and tabletop shooter and food stylist in town, I might approach someone like that. They do make things like room screens with rice paper, so there may be someone who could produce a huge sheet… but as the old pawnshop guy says down the street when you like a guitar… "getcher money out boy"...