trip to Iowa concerns!

I doubt you will find that "every" campground requires 3 night stays. I enjoy staying at Wal-Mart's and truck stops when I am just trying to get from point A to point B, but I have lots of batteries and a large inverter so I only have to run the generator in the evening while cooking and a bit more and then a bit in the morning before we leave. The drive will charge us back up again.
Are you going to need A/C all night in July? If so, you may end up running the generator 10-15 hours but that's still likely not too much more than it would have cost to stay at a campground.
Either way you will be OK, it's just a matter of what you want to do and where you want to do it.

Wing it!
There is many campgrounds and other locations. We have used Cabela, Pro Bass shops, Home Depot and Lowes.
OP didn't say exactly when his appointment is. My guess it is after the fourth by a few days. Just because he is leaving on the 2nd doesn't mean his appoint is on the fifth. That would be a quick trip from Florida.

Guess I'm a little confused... as usual. I do not see any problem with getting a one night CG on Wed 2 and Thurs 3 while in route as running your generator for 15 hours will pay for a cheap CG. I'd move my reservation up to starting on Friday the 4th as it's only 1200 miles to Moscow IA. Is Monday a Holiday too and when is your appointment?

Roadside rest stops and truck stop / plaza's. I do it all the time

Yes I would just plan on dry camping at truck stops or other RV friendly locations. I would also leave a few days earlier to avoid the holiday traffic. There are some places to stay up around the Mississippi River that would be fun to spend a few days.

Don't know what what route you are planning on traveling, but you might check KOA.com. KOA's are better at accommodating over nighters than State Parks.