In the meanwhile, I've been very happy with Charles Schwab's checking account. Free as in beer, you're allowed to overdraft with no overdraft fees, free ATM fees at all ATMs (including international!)
The next day I got a voicemail from one of their operators inquiring about my account with a number to call him back. The number went straight to him, and my account was straightened out in a few minutes. They also sent me checks, something I had never bothered paying for with my account at Chase.
And I haven't even put any money in the account yet. So far I'm very impressed.
I also have a USAA account, which reimburses up to $15 in ATM transactions AND has mobile deposit via Android or iOS.