The Bureau included a rather unique "permission" for e-billing in Comment 41(c)-4, allowing the use of electronically-delivered periodic statements when a borrower has provided E-SIGN compliant consent for e-delivery of other required written disclosure or statements:
4. Presumed consent. Any consumer who is currently receiving disclosures for any account (for example, a mortgage or checking account) electronically from their servicer shall be deemed to have consented to receiving e-statements in place of paper statements.
I would make sure, however, that the delivery mechanism and software requirements for the periodic statements conforms to those previously agreed to.