I would also suggest a F-350 with SRW or DRW. In 2005, the GVWR of the F-350 SRW went from 9,900 pounds to 12,000 with a gas engine, along with the new 18" rims and heavy duty brakes. I would suggest a 2005 and later V10 F-350 SRW, or if you have a heavy camper, then the DRW. However if you have been 'getting by' with a F-250 for all these years, the SRW F-350 might be fine.
Good luck finding one with only a few thousand miles on it. At 10 years old, even a 'low' mileage truck like your use of only 5,000 miles a year will put a lot of miles on it in 10 years. Sitting is also bad on the truck. A would be 'Jewel' with only 25,000 miles on it that my buddy bought needed a transmission rebuild, and many seals replaced, because it had sat for so long in a garage. Sure it looked great, but was mechanically in poor shape due to lack of use.
So a 10 year old truck might have anything from 70,000 - 150,000 miles on it. Even though your 'plan' is to keep putting 5,000 miles a year, you probably will get another 10 years out of your next truck, might as well invest in something that you really like.
I would not recommend another F-250. Even though the 2005 and later F-250 have a 2,500 pound cargo weight rating, and is a huge step up from your 8,600 GVWR F-250 now, it is not large enough of a step to carry a camper and stay within the GVWR of 10,000 pounds.
If you start looking at older 7.3L diesels, look for a dually. Some of the early F-350 duallies only had a 10,000 GVWR, that is way to low for a truck and camper! The 2005 and later dually F-350 has a very decent 5,500 pound cargo rating (including passenger weight) and probably is not needed with a light weight camper.
Yes the 6 speed was designed and added to the pickups with the more powerful 6.2L gas and 6.7L Diesel engines. Much more torque on both engines, so they had to improve something! Probably will get better mileage, but your insurance + gas cost will be a lot higher with a 2011 than a poor mileage 2005 with low insurance rates!
Call your insurance agent before selecting a model, and see if the rates will go sky high or not. You do not want the 'most stolen' or 'most likely to kill someone inside during a crash' vehicle.
BTW: The 2007 Ford Edge that I drive made it to the top mark of no drivers killed during the survey timeframe. So they counted the number of vehicle accidents and if the driver died or not. If the driver died, they collected data as to 'rollover accident' 'Single vehicle accident or multi car' and some other statistics. While the Nissan 300 sports car crashed regularly, the same car in luxury design upscale did not crash nearly as much, thus was rated much safer.
IIHS survey.
Good luck,
Have fun camping!
Fred.