That is a very large myth, snagging birds in mid-flight. First the greatest portion of their prey is arboreal mammals. I have had experience with WC emeralds (the big northern girl is WC) and if birds were a primary source of prey, I don't think they would take to f/t rats so readily. Emeralds are nocturnal, ambush hunters that locate prey with thermal sensors. Birds don't have a very large heat signature and would not likely be a good target as they flew by. Second, it's pitch black at night in a rainforest, below the canopy, what kind of birds are flying through forest tree branches at night?
They do take birds on occassion, but that is when they are forced to actively hunt, more than likely taking roosting birds.
Since you have a pair, I'm sure you have observered their normal hunting behavior. If you have ever fed live, you would see their very methodical stalking of prey with in the range of their anchor point. It would become quite clear that it would be impossible for them to hit a fast moving target passing by in seconds.
Unlike pit-vipers that extend the fangs out during a strike, emeralds front teeth act like meat hooks too snag prey. When they strike, the teeth stay curved back, sliding over the prey. When the prey reacts to pull away, they encounter the business end of those teeth and find themselves caught fast. Immediately the snake rolls the prey, wrapping it into their coils while using their tail section to anchor them to the branch. The whole point is to secure the prey and not lose it. Much energy is spent catching prey and if it is dropped, it's gone.
Humans have a natural reaction to pull back when bitten. This just drives those long front teeth deeper causing more damage. Getting bitten isn't pleasant and you bleed alot!
Craig