What the OP describes is an imbalance between the two legs of service that only happens when using the Hughes unit. The statement that he is unable to run an A/C or heat pump without the transformer is more telling than anything else since that should be easily accomplished with good service to the pedestal.
I wouldn't want to sit connected to a service that sagged to 104V under a typical oad. Your EMS is saving your bacon with that situation. My guess is that the campground has a problem with their campground "grid" and I wouldn't be looking for a quick solution to the problem. Sorry for the negative post on my part but you have all the good gear to camp with adequate or typical electric service and that isn't' being provided.