Minor correction....New Jersey has had many "circles" as they're called there, since at least the 1950's. Not as well-designed as you describe, they continue to be high-speed & dangerous. The higher "banking" in some (as on our exit/entry ramps) cause tractor-trailer & large SUV tip-overs, especially on slick roads. NO ONE slows down! Some are being altered. They have little in common with those I saw in UK.The smaller size and lower speed of a modern roundabout is a feature, not a bug. By making a smaller diameter circular roadway with superelevation (banking) against the direction of the curve, drivers naturally are inclined to drive much slower through the conflict points, dramatically reducing the risk of injuries and increasing the volume of cars that can safely enter the intersection. In fact, roundabouts can reduce the odds of crashes by substantial fractions, with some studies showing reductions in the realm of 80%.
There is a difference between a rotary and a roundabout. The first modern roundabout was not built in the United States until the mid-1990s (with the exception of a single intersection built in rural New Jersey in the 1930s that nobody realized had all the characteristics of a roundabout until that time). Roundabouts were developed in Europe in the 1960s as a safer, more efficient version of a rotary. See this link for more on the differences between the two.
Of course, unfamiliar drivers do have problems in roundabouts, but they also have problems in traffic signals, highway exit ramps, and all other types of roads. But the failure mode of roundabouts is a minor low-speed nonfatal fender bender, not a high-speed 90 degree collision. In places where volumes and geometries are appropriate, roundabouts are a superior technology, and I think they will work well here.
And an extremely high percentage of Disney drivers will be totally "unfamiliar drivers" since these are not common in most states.