I would suggest using the binaural beats until you feel super relaxed. Then slowly and casually take them off. Once you get that numb arms feeling, I would change your anchor to something more passive than counting. The counting could also be what is keeping you awake. Try the counting until you get the numb limbs feeling and then switch to observing the darkness of your closed eyes. Continue to fall into a deeper and deeper sense of relaxation. Basically, just sleep while watching the darkness.

You can swallow and blink, just try not to pay attention to it. If you have to swallow, just go ahead and naturally swallow. If you need to do a closed eye blink, go ahead. Just act as if you had never done it and carry on with the process. Fighting off swallowing and the urge to blink is often times much worse than actually going ahead blinking/swallowing.

Good Luck to you and if you have any further questions, don't hesitate to ask!