A major problem with the 6.0L was the head bolts, which in an overboost condition would lead to a blown head gasket, and eventually a cracked cylinder head. The 6.0L only has 4 head bolts per cylinder vs. 6 head bolts in the earlier 7.3 engines. The fix is to "stud" the 6.0 block and change the head gasket--requiring a full engine disassembly.
Ford issued numerous PCM recalibrations, and fuel injector, driveability and quality control problems were experienced. Fuel Injection Control Module problems caused by weak batteries caused problems when voltage in the fuel injection circuit didn't get multiplied from 12 to 48-50 volts to fire the injectors.
Ford also had problems with the EGR systems.
This is not the engine to chip to higher horsepower levels without substantial and expensive repairs to fix the problems inherent with poor engineering of this engine.