So, quitting my game then waiting to connect to the dark souls server is kinda BS. Is there a faster way to quit the game than waiting for all that?
More-or-less safe option: Force-quitting (Alt+F4 for PC; Cmd+Qon Mac; or just quitting to the dashboard on console) does the job, next time you will get complain about possibility of losing progress, but after like 30 quits like this I've never lost anything. DS should save your progress each time you interact with anything).
Safer (100% safe?): Alternatively, you can chose quit in the menu, then wait for "connecting to server", and only then force-quit.