Turns out it's quite simple, instead of passing expiry: 0 (which didn't work), just don't pass any expiry at all. Well, this explains why there wasn't many questions.
So instead of passing expiry with the flags like so:
$.cookie(key, value, { expiry: 0, domain: '', path: '' });
You just omit the expiry value:
$.cookie(key, value, { domain: '', path: '' });
And it works. It's such a simple thing, that it confused me.
But thanks anyway!