Hello Neighbor!
I'd say it's worth a try, I'd be very interested in how it works out. I do have a couple of comments.
There is usually a salt block out for livestock in our area. The manure can be salty enough to limit plant growth.
That said, almost any livestock owner would be happy to permit you to haul off all the manure you want.
You might see if you can get goat, sheep or chicken manure. They're a lot less likely to have contaminants.
I've been a fan of native grasses, and have some good clumps going in my yard. You do need to learn to recognize the non-native invasives, and pull them out before they go to seed. Be careful, or you'll end up with a field of foxtails, buffel grass, brome etc.
Do you have a good source for native grass seeds? That will speed things up a bit.
I think you should be prepared to do at least some watering, when plants are young and we have dry spells. Once it's established, it shouldn't take much.
Keep us posted, I'd like to hear how you adapt this system to your conditions, and how it works out.