Is your tire any easier to mount with no rim tape installed? That's the ultimate "thin tape". It's probably still a tight fit.
My Kinlin XR-300 wheels came with this thin reinforced tape, in a loop. I think it's about as thick as duct tape? I don't have a name for it.
I have the same problem on the Kinlin rims: a GP4000S won't slide around to line up the label with just one bead mounted and no tube installed.
I wrote up a
how-to for tight tires. The key is to just lift an inch or less of the bead, then slide over and repeat. It's fast and easy.
Like this: