I agree swapping the engine isn't going to fix the issue and likely isn't needed. It may reduce the blowby or increase it depending on the shape of the other engine.
White smoke on startup is a good indication of cold advance not working possibly combined with some non-working glowplugs. (It could also be timing, air in fuel, etc.)
There are two wires on the injection pump. The pink one is to keep the engine running with 12v on it. The other wire should be shared with a high idle solenoid.
Turn the ignition on but do not start the engine when stone cold. Check for 12v at the pink wire to make sure your voltmeter is working. Then check for 12v at the other injection pump connector. If you don't have 12v on it with a stone cold engine than the cold advance switch is bad or you have other issues related to it like wiring.
To set the high idle you do have to depress the throttle before starting the engine with the key on. Some people don't know this.
If you do have 12v you may have timing problems from a stretched timing chain and may need to advance the pump - best left to a "good" diesel shop. You may have a locked up advance piston in the injection pump. You can test this with a running engine by depressing the retard lever on the passenger side of the pump - the engine should darn near stall when the bottom of the lever is pressed in.
Air in fuel especially after sitting overnight. The GM manual really starts with "check for and eliminate any air getting into the fuel system".
Put a clear return line off the Injection pump to the fuel return rail. Look for air bubbles when running. On first startup have a friend crank the engine and watch for a bunch of air coming out. You are trying to figure out if:
1) you have a throttle shaft seal leak on the IP - common. Bunch of air after startup.
2) you have any suction leaks letting air in. Fuel filter assembly, fuel pump, fittings, fuel lines, tank pickup assembly... Constant air bubbles in fuel return line.
3) sticking injectors can let 'compression air' in resulting in the engine hitting, throwing the starter drive out, and then stalling. You really don't see this air in the system from the clear lines.
4) Restriction in fuel lines - but that would stall you out hot with vapor lock, yes, you can vapor lock a diesel.
A quick and dirty trick to see what cylinders are firing after a cold start is to use a IR temp gun on the exhaust manifold and look for a cold cylinder.
You can look for a Stanadyne dealer and ask them if they know a "Damn Good 6.2 diesel shop." This could assist with: diagnosis, timing, repairs. (After your compression test the shop that you took it to sadly doesn't know what they are doing on a 6.2. Sorry.)
