If your truck was turning 2100RPM at 65MPH in OD with the 3.73 gears, it will be turning about 2600RPM with the 4.56 gears.
That's pretty close to just shifting down a full gear in the transmission, and you have to listen to that all the time now, when you're not towing. It's still going to shift and when it does, you're going to have a conniption fit, because it's really going to roar. My estimate is about 3600RPMs in direct at 65MPH.
If it was purely the shifting that bothered you, this might work out, but for most people, it's the RPMs that make them uncomfortable.