25 years ago while replanting a 100-mile gas pipeline north of Reno in BLM lands in a cheatgrass area, at http://www.ecoseeds.com/greatbasin.html discovered that the exotic animal grazing had lowered the soil nutrients and organic matter below the thresholds needed for the local native seedling survival, that you can see at http://www.ecoseeds.com/good.example.html
By finding the soil nutrient thresholds in the top 5 cm, from around the seedlings of the desired native, and then testing the project area soils, and then adding fertilizers and organic matter along with the seeds, was able to get a cheatgrass-free planting in only six months, that remained 100% cheatgrass free for at least five years.
So my conclusion is that cheatgrass, instead of an "invasive" plants, the cheatgrass is what I call a "default" weed, only growing in soil too poor for the local natives and indicating poor soil conditions.
THE QUESTION IS, has anyone else used fertilizers to permanently eradicate other populations of cheatgrass, or added fertilizers to bring the soil nutrient thresholds up, so that the desirable plants are favored, and they can out-compete with the poorer-soil adapted weeds?