I didn't know there was any difference in Safari between C2 and C3's previews. Their fullscreen rules are obscure, undocumented and change pretty much every Safari release, so it's hard to know why that happens or what to do about it.
Browsers don't have permission to run a HTTP server, which makes it impossible to implement preview-over-Wifi in the browser, which is why we made Remote Preview instead. Since that's the only option, it would be better to try to figure out why it's not working at LAN speed for you and what could be done about it. It seems it's working fine for the vast majority of users, as complaints about it seem to be rare.