Might not count as the great plains, but Mark Sheppard's New Forest Farm in Wisconsin is a good demonstration of a similar approach in a different context.

https://newforestfarm.us/about/

Not to belittle the difficulty, but as someone who just drove from WY to WI over the last couple days... east of the Mississippi is drastically wetter than western MN+.

Yeh, there's a chicken and egg situation…

Having trees increases rainfall but need to grow the trees with little rainfall first!

Yes, the method applies anywhere in the planet. But for that you need to deeply understand the plants available for you, I mean those that are able to grow there in the beginning, native or not, here we use lots of african grasses and eucalyptus to start. There are a few people replicating this all over the world in very different environments.