Driving issues almost solved - but.....

Thanks Sunny Florida. I will check our weight next chance. It is free here in Oregon, we just drive onto a ODOT scale. Have done this many times.
A note on tire pressure. We have 2 stickers in the front driver door. One is from the manufacturer (Ford) and one is from Coachmen. The one from Coachmen states 75 front and 65 rear. I agree too much air can create some wander. I usually ran front tires about 5-8 lbs light on the truck camper.

Tire Pressures... I misread. There is simply NO WAY the correct Front Tire Pressure is 75-PSI!!! If your E350 has a 5000-pound GAWR Front, then 2500-per wheel comes out between 70 and 75-PSI. When E450 had the 4600-lb GAWR Front, max would actually be 65-PSI. At 75-PSI with a coach your size, you don't have any "contact patch" between tire tread and road. It'll wander and steering'll feel light.
So, print out the Michelin page. Load the RV as ready for a camping trip and go to the truck stop. If you tow a vehicle or trailer, hitch it up too. The truck stop's CAT Scale will give you Front, Drive, and Trailer weights. Drive will be Coach Rear and Trailer will whatever you're towing. Adjust pressures based on Front and Drive.
You may find you don't need to do anything more...
There's something about human nature where many of us will spend $1000 on chassis improvement parts before we'll spend $10 (which is what TA charges for CAT Scale) to see what we're working with. I'm not accusing you or anybody else...I was one of those. When I finally DID weigh it, I was shocked at how much MORE it weighed than any of my information would have indicated.

I bought a Thor 22E on the same chassis last year and also experienced problems with sway and wonder. Several people suggested front end alignment and said Ford would pay for it. They would not. I did contact Thor and they reimbursed me for the alignment because it was significantly off. My rig weighs about 11k lbs. The door sticker says the same as yours, 75/65. However, the Michelin tire chart recommends 45 front and 50 rear. I added a RoadMaster steering stabilizer. My first trip since the mods will be in 2 weeks. I will know then if they have made a difference.

Get a front end alignment!

You need to weigh the rig and set the tire pressures according to the tire manufacturers load chart. Ignore the sticker on the front door because the manufacturer of the chassis has no knowledge of the weight of the completed vehicle. The other key issue is wheel alignment. You need to take it to shop that can deal with alignment on a class C and have them set the caster as close as they can to the maximum. The alignment shop will want to set the caster close to the middle of the allowed range but that is not what you want and it won't help your wandering. Shocks won't really help with wandering. Once the tire pressure and alignment are optimized, the steering will be as good as it's going to get. It will likely never drive as easily as a car.

It's new, so we know the front end components are not worn. You've already done a lot. But have you had the front end alignment checked? I've heard told that Ford covers "one alignment" as if they know they can't guess how your chassis will be loaded.
I suggest you DO have it aligned but if it's at Ford, be sure they're equipped to handle, and actually understand, this Twin-I-Beam chassis. What we've learned here is that you do NOT want the CASTER set to "Factory Spec" which is at the mid-point of a range which goes up to about 7-degrees positive. Mid is about 3-degrees positive and we've found that 3 is NOT enough to make the steering want to come back to center. About the most you're likely to be able to get is around 5-degrees positive. That's because the same adjusting point also determines CAMBER and you'll drive Camber out of range with more Caster than about 5-degrees.
I say "equipped and understand" because many treat the E-Series chassis as a "Toe-Only" alignment. Caster and Camber are very important and need to be set correctly. Then Toe is set last. It's critical too, and how the Toe is set also determines if your steering wheel is centered as you drive straight.
Tell the shop you want Before and After printouts from their alignment system. It's normal for the Right/Passenger side CASTER to be a fraction of a degree more than the Left/Driver side. Don't worry if they don't come out equal, they aren't supposed to.

Thanks for the suggestions so far. Regarding tire pressure I had been fighting that so finally when to a tire shop and they found a screw in the front passenger tire. Repaired tire, check pressure on all tires - set them to ratings suggested in front door (75 front, 65 rear).
We then took a trip, only about 140 miles round trip.
Lot of steering issues resolved except for the wander issue I am describing.

Also look into Koni-FSD shocks. Same performance as Bilsteins but offer a softer ride when conditions allow.

It does sound like a wheel alignment might be in-order. That may help some with your steering wheel floaties. Also make sure your front tire pressure is set per the tire PSI sticker on the driver's door. The RV manufacture should have added one there. Over & under-pressured front tires can create some floaties too.

Assuming that you've weighed it & adjusted tire pressures accordingly, and that you've also had the front end alignment checked, next step is Bilstein front shocks. I don't own a Ford, but have seen many, many posts here singing the praises of the improvement this makes even on new ones.

Jim, "Just when I finally got a handle on life, the handle broke..."