First thing, split the upper, and lower. Notice how much effort is needed to draw back the bolt carrier. Closely inspect the gas key, and gas tube for signs of interference.
Next, cock the hammer (Lower, still separate from the upper), set it on auto, and with the right index finger pull the trigger. Guide the hammer down gently (or you may damage the mag well) without releasing the trigger, pull the hammer back, and attempt to drop it using the auto sear. Note the amount of pressure required, as well as signs of excessive wear, or interference with the bolt carrier. (Are you using a regged drop in auto sear, or is it a true M16 conversion? The more I read your description, the more it smells like a hanging or improperly installed sear spring, OR a bad DIAS. Bursts, having to repull while in auto, etc..)
Pull the buffer. Considering it's a M4 style stock, does it have the right buffer, and does the buffer go "kaclunk" when shaken? Note signs of wear, binding, or damage to the buffer tube from bolt carrier overtravel, or a damaged recoil spring.
Lastly, have you tried a diffrent kind of ammo? Some bad lots of surplus or cheap ammo will have a dramatic effect on cyclic rate.
Meplat-