It sounds to me like the large motor is struggling somewhat under that load, I would personally try an Extra-large motor to reduce that stress, you would probably need extra gearing through to increase the speed of the slower Extra-large motor
From what I know the EL motor is just a geared down L motor, so using gears to increase it's speed again will probably produce lightly more load due to the gears friction. You could use two motors though. Or be a cheater and use a non LEGO motor.
