My 2005 F250 pulled a 11K+ lb bumper pull toy hauler all over the western mountain ranges and the toyhauler was replaces with a 4000 lb truck camper with 8000 lb enclosed trailer in tow which also handled the job without fuss for 10 years and 120k miles. I believe my 5K mile service intervals at a shop that knew what they were doing kept that smile on face verses what some others experienced.
I am skeptical about the reason for the "bulletproofing" since mine was 100% stock except for suspension and wheel upgrades. This may indicate signs of neglect or abuse earlier in the trucks life. If there are any signs of a tuner being used, I would avoid any brand truck offered (unless free). I would still be towing with my 6.0 if I did not need additional payload.
The advice about poor starts or rough idle are a sign of problems with injectors or FICM, so this is an easy way weed through potential vehicles.
If you can find a F250 with the camper package, it has rear overload springs and a stabilizer bar which will make fifth wheel towing just as good as a F350 SRW, but you will be 2" lower with your bed rail height(which may be a good thing).