I have no experience with the "no peep" but based on your situation I would consider getting a peep with a larger hole/aperture.
But really, if you ever decide to trade up to a different bow you should strongly consider trying out a left-handed bow next time. The dominant eye should drive the choice of how to shoot. Although I am right-handed in everything I do my left eye is dominant so I shoot left with both gun and bow. You might think it would be a difficult transition but I found it to be very easy and I am able to shoot any weapon with both eyes open this way.