M.W.
The only covers besides wool that I have tried that don't contain anything you mentioned are the Cot'n wraps covers. I thought they were just "ok", but if you're trying to avoid what's in 99.9% of most diaper covers that aren't wool, they might be what you're looking for. They cannot be washed in hot water, because they are cotton and will lose their "waterproofedness"--they air out quickly and rinse well with cold water in the sink. Here's some info about them http://www.greenmountaindiapers.com/cotnwrap.htm
Lots of companies make microfiber/fleece covers, but I'm assuming since you are trying to avoid synthetic linings, those probably wouldn't work for you either.
Most covers are going to be bulky, unless they have the PUL in them. The Cot'n wraps are pretty trim, but if you have a newborn or little one who is pretty stationary, sitting on them in a wet diaper for a long time will cause them to seep through somewhat.
Good luck!
PS--Is there a specific reason you are trying to avoid PUL/vinyl?