The latest update to my Framer templates includes a fix for the full-page bounce on Mobile Safari, which I'm sure has annoyed many of us. You can grab an updated version of the templates from here: https://github.com/tisho/framer-templates.
In case you don't want to use the full template, but would still like a drop-in solution for your bouncing problems, I've broken out the script into its own separate repo: https://github.com/tisho/framer-prevent-bounce. You can see an example of it in use here: http://tisho.co/framer-prevent-bounce/example/index.html (load this on your iPhone).
Thanks to Jay Robinson for finally making me come up with a solution to the bouncing issue.