If you go into your game's settings, you can uncheck "Always show Clay.io login box on load when a player isn't logged in" so the login box doesn't show up when the game loads. Then just pass the user's name as part of the C2 action (ask for their name with a text input, and pass that value) - doing this should bypass the login completely, and just use the name you grabbed.
The Safari crashing might have been a fluke - I haven't had issues with it, but I know Safari and Chrome on iOS randomly crash a lot for me.
Can you email me (email@example.com) what gave you a hard time when you tried logging in as a guest or closing the window? I probably won't get notifications on this thread, so that email is best, or posting in the Clay.io community