I don't know how bad the symptoms are but I know that the 6.0 does not like to be lugged down past 1500 rpm on a hard pull. Even an automatic with locked torque converter tuning will rumble, growl and shake the truck if lugged at lower rpms. Keep the revs more in the 1800+ range and see if that helps.
Hopefully this is the problem and it's not something more serious like clutch/flywheel issues.