With T-posts as corner posts, you will almost certainly get some sagging from the weight of the fencing, tension in the fencing, and wind, let alone any ice or snow that may build up on the netting on top. If you don’t use wooden corner posts and really set them in solidly, I suggest you use guywires to brace them to keep them from sagging. By guywire, I’m talking about a wire that goes from the top of the fence post to an anchor in the ground in line with the fence. The guywires are a pain to mow and weed-eat around but I just don’t see how it is gong to fail to sag, especially if you only drive them in a foot or less. A wet snow or ice will build up on that netting.
12’ is a long span for netting or wire. I agree with driving a few posts in the middle of the run and stretching a wire along the top, but that probably will still not be enough to get the netting up out of your way. I’d consider driving your 7’ posts in the middle, then wire another t-post to the one you drove, overlapping them about 3’. Or you can use pipe clamps instead of wire if you wish. By overlapping them 3’ you will get a 4’ extension, plenty of height for you to walk under.