Today is the day to do it. Leave a guild after you have completed as much of the GE as you plan to do, and after a Battlegrounds Season is over and you have received your rewards. There is a very narrow window when it is optimal to leave. Usually, the trick is that the new guild has to let you in. You can't see any invitations that you may have until you leave your old guild. And a guild may send you an invitation, but if they get the maximum of 80 members at some point, the invitation that they sent you previously will be automatically deleted.
If you do join a new guild and it doesn't look like it is going to work out, do your GE and bail before the Battlegrounds Season starts.