What size is the return chamber on your sump?
Your overflow can't flow more than what it is given by your pump. If the overflow can really handle 800gph, you should have no problem pumping 656gph into your tank from the return.
And I'm confused, when you say 'keep the water level up'. Keep the water level up where? The water level in your display tank should be at a constant, and the only place where the water level changes is in the return chamber in your sump. The water level in the return chamber will lower as water evaporates, so you need to keep it topped off. If the return chamber is being sucked dry, it can only be one of three things: either the pump is too large for the overflow, the overflow is being plugged by something, or the return chamber is too small. What do you have in your sump?
It shouldn't be that complicated. As long as the pump gph is smaller than the overflow gph, you shouldn't have a problem. Also check your overflow piping for blockage.
Can you take pics of your setup?