Hi Chock full of nuts,
A few things stuck out in your post that might have shifted your setup.
Tires: Tires and how they react can make or break a stable rig. We know this changed. A few questions on them.
What brand, type, and size tire did you have before?
What brand, type and size tire did you buy new?
Being it is a F250 and you mentioned E load range, that fits right for the truck but not all brands/types load E range tires react the same.
What tire pressures on the truck, front and rear axles are you towing with? With the old tires and the new tires?
What is the tire pressure in the camper tires when you are towing?
This is a place to start and needs to be ruled out it is or is not part of the problem.
Your camper, I tried to find some info on it. I found this link which has the inside weight sticker empty
http://www.tomraper.com/rv/fairfield+oh/dutchmen+traveltrailer/14806/dutchmen+dutchmen+25f+liteYour truck is well match for that size camper. So the truck is enough for the camper and we can we rule that out. However there are a few other things that need to be sorted out to make sure the setup of the complete rig is optimized.
As was said, weighing the truck, camper and the bike in truck bed is for sure the right place to start. You need 3 weight sets when you go. And make sure the camper and truck are loaded the way you camp, with the bike in the bed.
You need the TV axles (front and rear) and the combined TT wheels on a 3 segment scale so you can get individual axle weights. This is a 3 segment semi truck scale setup. See here
http://catscale.com/how-to-weighHere are the weight sets you need to get, all axle by axle.
1. TV and TT hitched with WD engaged.(hooked up) Take a weight.
2. Don't move the truck from weight 1. Just unhook the WD bars. TV and TT hitched but no WD bars on. Truck is holding the dead weight of the camper tongue. Take a weight.
3. Pull off the scales, unhitch the camper in the yard, go back weigh just the truck front and rear axle. Take a weight.
Come back with those 3 sets of weights and we can help you sort them out.
This helps tell us and you a lot about how your WD hitch is setup and how the camper is loaded and balanced.
The bike in the truck bed, was any of the bike tires behind the rear axle of the truck or where both all in front of the rear axle?
Does DH have air bags on the back of the truck?
Explain what you felt in the truck when wind events where occurring?
You said DH slowed to 50mph and it got better, what speed was he doing when it was bad?
When the uneasy felling of instability happened, did DH have to make steering corrections because of it? This helps tell us how much the instability affected the truck and camper.
The TT, do you know if it was close to level when hitched up or was the front of the TT high or low?
I know, lots of questions. There are a lot of variables in what "might" be the problem and we are trying to help from a cyber campfire. The more cwe know more about your setup, the better we can help.
Sometimes the problems are simple and you adjust 1 thing and all is well. Other times it takes more work. The key is, all areas of your truck and camper are setup optimized the best they can be. That is the best way to do this, then you know what is right and what needs help. Once the setup is optimized, your odds are much better that small shifts in loading the camper or the truck do not make large handling problems.
Hope this helps start you and DH on the road to getting a stable towing camper back.
John