As you have discovered and others confirmed, the dead weight of any type of netting hanging free in open space is going cause it to sag. So it has to be supported. You have to find some way to transfer the vertical weight of the netting hanging down in the middle over to the load bearing sides. You can do that a couple ways. If you use a wire or cables, it too is heavy and it too will sag unless it is stretched to such a high degree it won't bend sideways. That takes a lot of tension, so that is where the sideways pulling screw-in ground anchors come into play. You see these on any powerline where it has a bend. The guy wires run from the ground to the top of the powerline pole to create a sideways pull to keep the powerline from sagging. A variation on this theme is essentially what they do with big top tents. Short poles around the edges, high poles in the middle with ropes between those running to the edges and guyed out to tent pegs or screw in anchors. In this case, the high poles in the middle support both the dead weight of the tent and also the rope running over them. If you stick with your T-post idea, this is what I would do. The wood poles need not be fancy. Go find some tall, straight black locust trees about 2 or 3 inches in diameter and cut them about 10' long. Bury a foot or so in the ground to stabilize them.
Option B is to consider scrapping the T-post idea and go to a system of bolted together posts as seen with chain link fence runs. Use your wire and whatever netting you want to use on top, but spread it over a frame made from these bolted together parts. In this case, the part in the middle is a gable style roof where the center ridge pole is supported by poles that bolt to it, then run down to the sides.
Option C is to consider doing the same thing, but framing it out of 2 x 4 treated lumber. In this case, you could scrap the high gable style center ridge pole and run 12' 2' x 4' rafters across the top to carry the load to the uprights. You can make them level but that may not give you as much head space as you would like. So you could one side higher (shed style) or if you don't mind the extra complexity, you could make it a gable roof. The advantage of wooden roof supports is if you decide you want to put on a roof vs. just the netting, you already have the frame for it.
Option B is to consider scrapping the T-post idea and go to a system of bolted together posts as seen with chain link fence runs. Use your wire and whatever netting you want to use on top, but spread it over a frame made from these bolted together parts. In this case, the part in the middle is a gable style roof where the center ridge pole is supported by poles that bolt to it, then run down to the sides.
Option C is to consider doing the same thing, but framing it out of 2 x 4 treated lumber. In this case, you could scrap the high gable style center ridge pole and run 12' 2' x 4' rafters across the top to carry the load to the uprights. You can make them level but that may not give you as much head space as you would like. So you could one side higher (shed style) or if you don't mind the extra complexity, you could make it a gable roof. The advantage of wooden roof supports is if you decide you want to put on a roof vs. just the netting, you already have the frame for it.
