Answer:
Incentives are attractive to me, but I also want the bank to tout its reliability and security. Without those last two, I don't care that you waived a fee for me or entered me in a contest to win something.
If I were pushing this in a bank, I'd start at new accounts. Get feedback from your staff on what your customers like, dislike, and what mitigates their fears. Turn that into an ad campaign for current customers.