Hi there, hope you are enjoying BYC!
With E fencing (a great choice btw) the problem is not (ground) predators like coyote coming over, but the hen that insist on jumping over into the waiting mouth of the fox and such.
Bait it... so the predators get their first taste of E fencing and watch them tuck tail and RUN!
Four foot fences contain MOST of my chickens. I have had about 3 out of several hundred that would insist on going to the neighbors. I clipped wings because monkey see chicken do and one will teach others their bad habits. When wing clipping wasn't enough to stop a wayward hen (as they are safer IN my property with wings clipped than outside of it with full flight feathers) I re-home them to someone else or the freezer if need be. One of my roosters got a close bilateral clip to keep him in the stag pen. Single sided clip didn't remove enough lift and the off balance was irrelevant.
If cost or moving doesn't stop ya from going taller... when it comes to poultry... it seems as though bigger is almost always better. For what it's worthy though... an animal that only touches the top of the E netting... will feel nothing. They MUST be standing on the ground.