What is the year and model of your vehicle? That will help folks respond with better answers, since the 6.5L has used both mechanical and electronic injection pumps and turbo waste gate systems.
You probably have more than one issue going on here.
First, black smoke = lack of air, which is usually a result of low boost pressure. You say you have boost, how have you determined that? Do you have a boost gauge? The factory 6.5L turbo boost waste gate control system is prone to failure. It will allow boost at low RPM, and then open the waste gate and all allow exhaust gases to bypass the turbo and quit building boost right when you need it the most. Black smoke can also be the result of a clogged air filter. Either lack of boost or clogged air filter will also result in low power.
Second, oil consumption. What is the rate of oil consumption? Do you have any blue smoke coming out the exhaust? Black smoke is fuel, blue smoke is burning oil.
Casey
1995 K1500 Tahoe 2 door, 6.5LTD, 4L80E, NP241, 3.42's, 285/75R16 BFG K02's; 1997 506 block; Kennedy OPS harness, gauges, Quick Heat plugs, and TD-Max chip; Dtech FSD on FSD Cooler; vacuum pump deleted, HX35 turbo, Turbo Master, 3.5" Kennedy exhaust, F code intake; dual t/stats, HO water pump, Champion radiator; Racor fuel filter