Our club's level is medium. Some players recieve often a serve to the halfcourt. And they make it not so fast as they should, so I can intercept a shuttlecock before he goes down below of top of the net. But I can cover only one side - forehand or backhand and other side leave to the my partner, which stands behind me. So which side is it better to intercept for a net player - forehand or backhand, taking into account that my partner agrees to cover other side? In my opinion in mine a case such system is more effective, than to play by a shuttlecock when both partners rush in one side.
I can't understand your post, only the receiver can receive the serve. If it's covering, it depends on your serve return, do you do it high or low. not decided by backhand or forehand. if it's low, enter front-rear attacking formation, but if your serve return is high, like a clear or lift, then enter the side by side defensive formation. your partner should initially be near to the middle line when you receive the serve.
If you want to pick a side to cover, safest is to pick the side of the court you're serving from. Then your partner will cover his side.
If your opponents always push, you can divide the coverage into 2 halves as you describe. But your opponents may be able to observe your predictable pattern, and choose a return that maximizes the damages. Or you could observe their habits (if any), and anticipate (i.e. move faster towards one side, or the other). You take only 1 step away from serve position. That's probably the time you have. They may notice you anticipate them, and they change. You should, too. If you can't observe any patterns (in other words, they mix it well), maybe you could also randomize your coverage; bias to one side or another randomly. If they hit to the same side you choose, you ought to have an advantage. Just make sure you don't overcommit and get your side into deep trouble. In this case, your partner would be the safety net and may have more to cover. But I think you'd become a bigger threat to your opponents. Would like to hear what other have to say...