My recommendations, the cheapest route would be do all the labor yourself to remove the turbo, clean, and replace the unison ring with a stainless ring and reinstall. I don't think this is the route your wanting to do. It isn't that big an ordeal for a novice mechanic with help from youtube.
I believe the best route to accomplish your goals would be to just buy a new Garrett GT3782VA and either replace yourself or have a mechanic you like do it. The latest Garrett turbos are new manufacture, not rebuilt, and have many updates that prevent the issues of the turbos of the early 6.0 years. They have come down in price to around 700-800$, which in turbo world is cheap. The advantage of the new Garrett in addition to the improvements is that it will perform exactly the same as the original (see below).
It's fine to upgrade turbos via a fully designed unit like the KC 1.0 or one that a shop has souped up however there are drawbacks to consider. First is cost, many of these can be at least twice as expensive as a stock Garrett and you will need to tune your ECM for them, even on a stock motor. Aftermarket turbos for the stock to mild powered motor offer significant gains in efficiency, but the stock ECM will still configure the VGT (the veins in the turbo) duty cycle the same as the original Garrett. In short, it doesn't know the turbo is different. This often results in the new turbo actually producing less manifold pressure through out the power band (think daily driving throttle positions vs wide open throttle) and causing the engine to run fuel rich (black smoke) and less power. Long story shorter, if you install a not factory turbo, even though it is a drop in replacement, it will still likely require some tuning of the VGT regime to gain any benefit or even regain lost performance. All of this is less obvious in the F series trucks as they have different factory tuning than the vans, but it still happens. Lastly, if you go this route and you live in a location that is "excited" about smog testing that will add complexity to this as well. Just factor that in.
I'd go with the new Garrett and call it done.
2005 SMB RB 4x4 6.0 PSD
A rocket on the pad is safe,
but it's not what rockets are built for.