As I said earlier, I tried to get the Arduino to keep track of time on its own, to denecessitate the DS1307, which in turn would denecessitate using the USB battery. JeeLabs's/Adafruit's RTClib was too confusing and overkill, and my simple implementation seemed to be picking up mains noise on the button pins (even with internal pull-up, and even when I gave them zero-ohm pull-up/pull-down). I haven't made any progress on this since then, but the other week I ran across an ATmega328P-based wristwatch called ChronosMEGA, the instructable for which is extremely detailed. I'm reading through that today to try to learn better ways to do what I want to do. It also claims 11 years of standby battery life!