Great questions.
I assume you already know this, but for those who don't, the government didn't simply "take" the ranches that made up White Sands.
It only condemned the small portions of the ranches that the ranchers owned in fee simple, refusing to pay for the value of the ranch as an operating concern (i.e., the fair market value of the ranch).
The government also did not actually condemn the fee simple. It rather only condemned a 10-year lease in the fee simple, and then at the end of each 10 years, condemned another lease. That resulted in the ranchers only getting a tiny pittance from the government. They had not been rich as ranchers (ranching at White Sands is hard), but they made a living. The amounts paid to them by the government forced them into poverty.
I know this because when I first got out of law school, my firm was representing those ranchers and the State of New Mexico in an inverse condemnation action against the government in the US Court of Claims. We won, obtaining a judgment against the government in the multiple billions of dollars.
The government immediately offered us a settlement in which it agreed not to appeal the judgment in return for our agreement to join in a motion to the Court not to publish its decision. The government did not want the decision published because it had done the same as it had at White Sands all over the US during WW II. The only specific location I heard where it had done the same was Fort Hood.
I was googling around the other day and think I came across the published opinion, so the Court may have rejected the joint motion of the parties. I'm not sure. My role in that case as a brand-new baby lawyer was minimal, at most.