I don’t use porta grazers because I’m very happy with my nets, but sure, they tip over. Horses stand em back up. If you don’t want your horse to tip it and bounce it around the stall, get the corner model, which can be secured.
I hang my nets so they’re just off the ground. Picture a full small bale, on end, just off the ground. Horses can choose to eat anywhere along the length of the bale. The usually choose to eat toward the bottom, near the ground. I have had zero issues feeding my horses like this for…man, it’s been a decade.
I use nets outside over the winter, too. They’re hung a little higher, from the top rail of the fence. Those nets hold a half bale each. Also no problems with that.
Nets are overall cheap to try, and they absolutely kibosh the whole bedding in the hay thing you’re seeing now. It’s a very reasonable place to start. See how it goes. If you don’t like it, try something else.
I feel like you put a lot of pressure on yourself to find the one true BEST answer right off the bat, and that’s just not often how farm stuff works. It’s okay to try something, decide it’s not quite right, and try something else. Nets are cheap. Start there 