I know I've seen vinyl backdrops for sale - might take some searching. I'd guess they need to be rolled though, which would put you back in the seamless paper hassle category. But maybe not.
I use a garment steamer for greenscreen shoots - it works pretty quickly and I've used it on white muslin for the smooth look. I just have the consumer model, runs about $150 and gets a lot of use for apparel shots. The hanger-pole pops out which makes it easier to transport. You can even take the hose off with an adjustable wrench which makes it even easier (and you can drain the leftover water from the hose more easily when it's off).
They're really handy things to own, it's much quicker to do a quick de-wrinkling of a shirt with one, if you don't need that "pressed" look. My wife's hijacked it to the laundry room.