If it were me, I would call Z tech support/customer support, just to be on the safe side (regarding login and payment issues). In my recent experience, tech/when you get the right one, has been very helpful. Today being Friday, I would call before end of day, or you will have to wait till Monday to get anyone on the phone.
There are two places you have to change your email on Zazzle. One is your preferred payment method. I did recently change mine, but both my old and new email are still listed on PayPal. So far, no problems with getting paid on schedule.
Many thanks for reaching out. As @idraw has suggested, I would advise getting in contact with our Customer Service Team here. They’d be more than happy to answer any questions you may have on changing your email address 🙂