If we move a bank but have a large supply of preprinted statement paper with old address, does Reg. E and other applicable regs allow a certain amount of time to update address?

No. You should replace the outdated disclosures or you can add a statement message with the correct address to all statements until you exhaust your old supply.

That said, I'd consider this a low-risk technical violation.

Try to make sure that a phone line is forwarded and mail gets forwarded, too.