Last year I did a google search for vermiculite and asbestos. What I found was that the asbestos problem was mostly in vermiculite from the Libby mine, which is closed, and present vermiculite supplies are asbestos free.
I've never been convinced that sphagnum is any better than damp paper towels. I've used paper towels and consider vermiculite better because some badly dehydrated eggs pulled through in vermiculite, eggs that I believe would have died in any other medium I've used. On the other hand, I've never used perlite. So vermiculite's mess is endurable, for me. YMMV.