In your scenario, tonque weight is much more likely to be a deal-killer than tow weight or having enough power with the 5.3.
You mention a "dry weight" of 7,501 lbs. This sounds suspiciously like a quote from a "sticker" on your Jayco. If so, that's a very unreliable figure--the last piece of data I would use to make a decision on a new $35k-$50k TV.
Bottom line, if you haven't done so already, I'd highly recommend towing your Jayco to a scale with your current truck and getting it weighed fully loaded, vacation-ready. Before you leave the scale you should have your Jayco's tongue weight, axle weight, and gross weight, fully calculated (tongue weight + axle weight = gross weight).
If you go with the 2014 5.3 and the Jayco, I'd be very hesitant about choosing the 3.42 rear end. Odds are your Jayco weighs closer to 9,000 lbs. vacation-ready. The slight loss in fuel economy using the 3.73 rear-end pales in comparison to the potential strain the Jayco would place on your driveline with the 9,700 lb. limited 3.42 rear end. The 3.73 rear end would give you a much-needed safety margin of 1,500 - 2,000 lbs.
Just my two cents . . .