You can incent existing account holders to go tree-free, but your ESIGN "license" is conditioned on the customer retaining an option to continue the existing (paper) delivery method. Unless you have a valid ESIGN consent, nothing you e-deliver counts as being "in writing." If the Reg E and DD disclosures in your statements aren't "in writing", then you have systemic violations of those regs.
In the future, you can revise your online banking agreement and condition this service on e-delivery. Customers who demand paper will not be forced into e-delivery, but at the cost of losing their option to sign up for online banking service. It's up to you to decide whether compulsory e-delivery is a good business decision.
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...gone fishing.