At least as of a few years ago, though, Sovereign credits weekend deposits/debits in whatever order they choose. Meaning, they once bounced 6 debits (and charged us $25 "overdraft" for each one) on a weekend, because they wouldn't credit a cash deposit I'd made Friday afternoon (at a teller window! but it was officially "after banking hours" even though they were open) that would easily cover all the payments.

Never used their billpay, though. I've actually been very pleased with Bank of America for all your requirements except the multiple checking accounts--but I can move money from checking to savings with no fees.