At the present time we don't have UI to set your main account email (ie the email that you use for password resets). If you'd like to change that please contact support and we'll work it out.
Creating a "for invoice" contact will change the email associated with your account in our billing backend (Stripe). At this time it won't update the other contact info that appears on your invoice, but its a planned feature. For now, we're happy adjust that for you upon request. Our support will work with that invoice contact for billing inquiries only.
We'll consider any other contacts you create to be valid contacts for support inquiries.
We do recommend that you create a contact with an external email address, or better still use an external email for your main account contact, so that we can contact you under the conditions you described.