it seems whenever you read an article about large events, the large wheels are always described as one of the most popular rides. Who all exactly moves a very large wheel (bigger than chance giant wheel) and what do you know about them (loads) ?
Here is what I could find so far from what I read as quoted by the show owners in news articles:
Reithoffer has a Dutch Wheel they move (120 feet high - 4 trailers) purchased in 1986
Strates (126 feet high - 4 trailers)
RCS has 3 very large wheels, one called the Big Wheel (108 feet high - not sure number of loads), another called the Grand Wheel (108 feet high - not sure number of loads) and also the La Grande Wheel XL (164 feet high - 22 trailers) purchased in 2017. RCS had all 3 set up at Houston.
Wood/Wade Sky Eye Wheel (150 feet high - 12 trailers) purchased in 2017
Powers Parthenon Wheel (108 feet high - 4 trailers) purchased in 2016
Talley Amusements Giant Wheel (108 feet high - 4 trailers) purchased in 2018
are there others?
As far as I can remember you nailed it pretty much, I know there are several shows carrying smaller European wheels that only travel on one trailer. But here is some history as well as to who had what if your interested:
Deggeller had a Dutch wheel for a while (80s). Reported as 110 feet high, first appeared at the FSF and came with a straight truck from Europe but it had to be cut up due to pollution req. here in the USA. That wheel now resides at Knoebels park in PA. Traveled on 4 loads.
Conklin had a Dutch Wheel up till they became NAME. It was 4 loads and last I heard it was junked sadly.
I have seen pictures of a dutch wheel in an Amusements of America company brochure, but from what I understand they never owned one, and I have not seen that type of wheel again or know of anyone who had it in the USA, so could have just been a picture they used.
Interesting note, when Strates (and I believe Deggeller and Reithoffer) first had their Giant Wheels it was actually 5 loads. The fifth load was a dog house and either carried spare parts or was a bunk house. But they soon dropped that extra load to reduce costs. I can remember seeing it parked behind Strates wheel and the guy inside operating.
Also, I know Reithoffer's had a back wall, but I think Deggeller's did as well although he never used it that I saw.