Unlike regular large hole hay nets, as long as your ponies are barefoot I would not worry so much about feeding with the nets on the ground. The holes are too small for them to get a foot in, especially if you’re using a 1-1.5" net. I have several friends who throw 3-4 flakes in several small hole nets and toss them around their paddocks in the winter. Spreads them out more like natural grazing and they aren’t standing around a round bale all day squabbling. Do make sure you inspect the nets daily to make sure they haven’t chewed holes in them that they could put a foot through.
If you are concerned, you can put the net in a tub, but they will likely figure out how to dump the net out of the tub unless you anchor it (perhaps a muck tub tied to a fence post, and the net also tied to the post?).
My horse is shod, but does not generally paw. In her stall she has a net to make sure she has hay as long as possible. I choose to hang her net off the ground, but below her withers. I would not put the net right one the ground with her shoes on. Outside, she has loose hay or a round bale to eat off of.
Without using nets, your options are limited to a basket like the porta-grazer, but those options need to have a spring-loaded base to bring the hay back up to the top as they eat it. I see lots of plans online for boxes and such that will hold a full square bale, but I’m not sure how the horses are supposed to eat the bottom two-thirds of the box contents when its out of reach.
In terms of tugging on the nets causing issues, if they figure out how to use the nets properly, they actually don’t need to try to rip chunks of hay out. If they’re having to pull hard, they are either biting hay & the net and just pulling, and unfortunately there isn’t much you can do to teach them to not do that. If they’re nibbling and still having to tug, your nets are too packed full, which actually makes them more difficult to use.
I also prefer nets on the ground where possible, or hung in a corner, because they don’t swing around and they don’t have to chase & tug on them as much.