Sounds like the BEC can't provide enough current and is causing low voltage protection on the microprocessors to kick in causing a continous reset state while the servos try to move.

To run straight from battery voltage just cut the red wire on the servo connectors from the servo to the receiver and plug the servos end into the battery. Though check that it can actually take the voltage first. If they can't take the voltage try moving one servo onto the other ESC's BEC (as with the battery voltage mod I described above but plug it into the unused BEC).

Last ditch effort: Shove a higher amp VReg in just for the servos.