Prior to the battery swap, I had disconnected my battery multiple times while tweaking/moving my amplifier and wiring. Also using the reset on the unit itself, etc to no effect.
I can confirm it starts up every time now since I've put in the new battery. It is an almost 3 year (440CCA?) vs brand new (850CCA) battery though, heh. Though I had seen startup hesitations/long cranks intermittently in the past.
As for better gas mileage, the ECU does get reset if you leave the battery disconnected long enough.