Try removing all the glow plugs and then cranking the engine over. This will release compression and allow the engine to spin over faster with little resistance. Check to see if any liquid starts shooting out the holes (some fuel spray is normal if the injection system is working properly); it kind of sounds like the motor is hydro-locking, which would be strange to happen AFTER the engine cranks for a bit; if the cylinders are filling with liquid (such as engine coolant), I would expect it to happen from sitting still and leaking into the cylinders slowly, not after the engine is cranking over. I've also seen bad rod/main bearings cause this symptom, where the engine will crank normally for a few revolutions until the bad bearing heats up and seizes the crank; after it cools down, it will allow the engine to spin over again until it heats back up, etc.
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