Actually, FORD has done the tuning to that engine, as they did with the IDI6.9/7.3 before it, and the VT365/6.0 and the 6.4 after it. Ford has NEVER to my knowledge used an IHC tune in there trucks, other than in the 650 series. The max HP/Torque in the IHC for a T444E was 235/660, same with the VT365. THey had lows in the 175/450 range IIRC. My IDI 7.3 in my IHC is the top HP.torque at 175.335. Ford advertised it at 185/385.
Can one punch up the T444E, I'm sure you can, but the question will be, at this point in time, with out a complete rebuild, you may only blow the motor up that much sooner. IF you rebuilt it, then I would say yes, go for a bit more HP. torque etc. But with a close to 15 yr old motor.....I would not do a thing to it.
Marty