I would get the 20% battery life remaining pop-up message on my iPhone toward the end of each day, so i bought and installed the higher-capacity 1600mAh battery as well and even after 2 weeks of charge discharge, i still see similar battery life to my original (stock) battery. I am wondering if there is something you need to do to get the phone to realize the battery has been replaced.
Did you solve your problem with the new logic board?