Mega2560 regulator is only rated for 800mA; the 2560, 16U2, other chips & LEDs all need some of that. If you try to use more, the regulator overheats and shuts down. If the voltage at the barrel jack is higher, the regulator overheats sooner, so the current must be lower to prevent that.
When the regulator cools some, the processor restarts, which can look like a delay, probably of several seconds or more.
Can you draw a picture of all your pieces and how they are all connected?