I wouldn’t count on getting a site in Scholler with hookups but you never know. I’ve tent camped with my CPAP using a large battery pack without issue so you don’t have to restrict yourself to the 24-hr gen area if you can’t get a hookup site.
Only small coolers are allowed — the list of what’s prohibited is here
https://www.eaa.org/airventure/plan-...ohibited-items Wagons aren’t expressly prohibited so I think you’re good to go if you want to use it, but as you surmised you can forget about trying to load it on a tram. We ride our bikes to the gate so we only take a small backpack, water bottles, and our camp chairs to keep the load to a minimum.