First, non-cat cut tarps are more difficult to set up nice and taught. That's why there are so many cat cut tarps...
Second, the asym tarps are even worse for keeping nice and taught as the force vector's don't exactly counter each other.
Third, it needs to be suspended separately. Get rid of the mitten hooks and plastic ring. Tie directly to the tarp pull out and the trees, not the hammock suspension. Keep everything else off of the hammock suspension as well.
When you tie to the trees it needs to be very tight.
The guy-outs also need to be pretty tight and play with the angle to get the lines of force as nice as possible.
The problem is that, eventually, it will stretch and get the slack back. You can use tensioners to counter this. This will also happen with a continuous ridge line set up. These methods will lessen the amount of slack but may not totally get rid of it; it's just a matter of the design.