Could a decoupling cap cause this? Should I add a resistor in between the boards vcc and the controllers battery pack?
No, and no.
I suspect the additional current from the 2560Mega is the culprit. I assume you are feeding the battery positive directly to the Mega +5 header pin? (Not through the barrel power connector.) Looking at the schematic, you have 2 microcontrollers to power, several LEDs, and various pull-up resistors. My guess is the Mega2560 just takes more energy to run.
Did you upgrade from the atmega328 to the atmega2560 due to I/O pin needs of because of SRAM/flash requirements?
Ray