Camper pitfalls

Should have bought a long bed dually then! Simply put, you can add all sorts of stuff, but it will never change the trucks numbers from the mfg. GVWR, GCWR, RAWR,and tire/wheel load ratings could all wind up being exceeded with your intended load.

Make sure it's a short bed camper.
Ones with no vertical overhang in back help a bit when towing as you sometimes don't need as long of hitch extension. What u need for hitch ext depends on the camper and trailer.
Likely need to shore up the rear suspension. Most slide out campers are around 4000lbs. Tires make sure in the 3600-3900lb range.
Yes you'll exceed your payload rating, but the truck will handle a camper and modest trailer with relative ease.
Keep an eye on tongue weight. We don't know what your trailer is.

I own a 2012 Ford F-250 short bed with the 6.7 I have a AF 811 that when loaded is at about 5K and I pull a 7.5K boat and trailer with no problem. My AF sticks off the back of the truck about 32 inches and I am using a supertruss hitch and extension. My boat trailer tongue weight is 750 pounds. Now with that said I have made many upgrades to handle the weight. I have airbags, I have upgraded both front and rear stabilizers, I am using the torklift spring additions, and I have upgraded my wheels and tires. It took a little bit of time to get to find the sweet spot with the air pressure in the bags but now it handles really well. I have put many miles on it over the years with no problems.

Hmmm....not much info about how heavy your truck camper may be.
Regardless of the size of the truck camper the 6.7 won't have any issues pulling the load.
With a 3xxx lb payload can we assume the F350 is a SRW truck ??
The F350 SRW has 7000 rawr which includes tires/wheels and the rear spring pack. These trucks can carry in the 3800 lb range before exceeding the lessor rated of those components.

What size/brand TC's were you looking at ?

Long bed all the way. Dually for serious traveling with a tc and a trailer.

The biggest pitfall is buying the truck before buying the truck camper. You've already done that. It's ok though ... most people do.

Go as light as you can on the truck camper. It will be easier to tow if you also go as short as you can and doesn't require a hitch extension. Tires are the biggest limitation. You could go 19.5s, but you can't air them down for the beach. Better shocks and adding good sway bars will help. To level, you can use air bags with extended bump stops or stableloads, timbrens, supersprings, or stableloads by themselves.

with that truck you can find Many Campers without slides that will fit within the truck weight limits.

Best thing you could do is go trade it back in for a long bed truck.
The parts on your truck are all just as stout but you're limited to very short campers and your weight distribution will be far from ideal.

What do you mean by "slideout?"

Are you talking about "slides" which are sections of the camper that extend from the body to provide more living space?

Or, are you thinking "slide-IN" which is less-common name for a truck camper?

If you are willing to go with a lighter, less appointed camper, you can easily do what you want with no suspension modifications at all. There are many truck campers in the 8' floor range that have all the basics (i.e. bed, bathroom, kitchen, TV) that don't have slides and will run in the 3000lb range loaded, leaving you plenty of payload for a 5000lb trailer tongue.

I'm getting to the point where I'm about to say "ratings be damned." We've got people running around with 2500lbs on F150's, 5000lbs on F250's AND towing a trailer... They seem fat and happy, so apparently the ratings mean nothing.

Carrying an Arctic Fox 811 will be within your tire capacity, but it will require a 28" SuperTruss and the 500-750 lbs of tongue weight will take you into 19.5" wheel capacities. I did this successfully with my F250 and a heavier trailer regardless of the nay-sayers on this forum that are contrary.

The problem will be that 19.5's don't have flotation for loose sand use. You either need to find a truck camper that weighs 2500 lbs dry so you can tow the trailer and stay with your current wheels or switch to the OEM wheels in sand with only the camper and only tow with 19.5's swapped in.