Is the 6.2 guaranteed for x days and you have seen it run? Or is this a standard unknown take out engine that could be full of sand/cracks/etc? The 6.2's can be had for double the price, tested, and have a short warranty. Myself I hate to pull a bad engine back out. I have looked at enough bad non-running 6.2/6.5 engines including one that the intake was full of rain water.
The military pull outs should have the cylinders deglazed and new rings put in. IMO they don't get run hard enough to seat the 2nd ring and when you get it is it too late to get it to seat/break it in.
You 6.5 swap is missing one critical part, the turbo! No oil to where you lost the bottom end also means the turbo bearings are unfit for further service. The oil cooler is also suspect depending on what reached it with the last gasps of oil. You can find a cheap GM3 or 4 around depending on your budget. Or get something better. Maybe a little exhaust work and go NA.
Your tuner can help you use the DB2 on the 6.2 with what you have.
You can use most of the 6.2 including the heads. I would recommend using 6.5 precups NA or turbo as the 6.2 precups limit you and smoke like a freight train in a tractor pull.