I wouldn't want a srw even on a 4K camper. The high center of gravity weight is way different than hauling a bed of concrete blocks. In an emergency collision avoidance situation it's coming over. Same deal for high winds. I've driven south on I-15 from Vegas where the side winds had me white knuckled to the steering wheel with my poptop. SRW trucks with heavy campers were in the right lane going 45 mph with their flashers on. A dually with a big ass camper passed me like I was standing still. They're a hassle unladen but there's nothing like the two outboard tires for stability.
^ This.
Been using a cabover camper for many years now. Now on my third pickup under a camper. The first two were SRW...I'm a slow learner...and now the camper is on a DRW. Night and day difference in stability. Keep in mind the top of that camper, especially if you have an a/c unit on top, is close to 13' above the ground. So - do you plan to take it off highway? A dirt road just a little bit off-camber and you'll swear you are about to roll. Not to mention what happens if you get a flat, especially a blowout, on a rear tire, with a tall 4000 lbs in the back of the truck. I went dually about 10 years ago and couldn't be happier. The difference in stability is amazing. I'd be ok putting a pop-up camper on a SRW but not a tall hard-sided camper.
As far as gas versus diesel, that's a personal choice. Either one will do the job, especially with the new gas models. Personally I hate the sound (and even just the thought) of an engine thrashing along at 4000 rpm when it could be idling along at the same ground speed doing only 1800 rpm. That's the difference between pulling a load with a gas engine and a diesel. One of my rigs has the 6.8 V10 gas engine and driving it for a day in the mountains leaves me feeling tired just from listening to the engine and watching that tach soaring. I know that those high rpms won't hurt the engine enough for me to worry about it for the years I own the truck but still........
The photo below was taken ~ 50 miles from the nearest pavement. So yes, as long as you use your head you can take a dually off pavement. Another thing - the below setup (Dodge/Cummins), pulling the Jeep on a trailer, still nets me 13-14 mpg. If I tried that with the gas engine I'd be lucky to get 10 mpg. So look around. You may get lucky like I did and end up with a low mileage diesel. Any Cummins built before 2007 will not have all the pollution control crap on it and will last forever.