An amp draw test on a warm starter is not going to find a hang when it is cold unless it is in the armature. If it is a mechanical drive problem it may only show cold. Some problems like that intemrittent hang in the starter require disassembly to see or just replacement to cure. If it only does it cold it could still be a battery issue or more likely starter.
The copper washers seat the injector in the bore and unless they are loose it is not going to leak. Clearances are tight enough carbon will stick the injector in the bore, diesel is not going to easily bypass it. The o-ring is above the injector port from the cross over tube and will keep the fuel in the head return gallery out of the oil and has nothing to do with white smoke on start up. You would be making oil if the o-ring was bad.
I GUARANTEE if there w2as enough fuel in the cylinder to hydro lock it even a little you would know something is wrong. You would likely run from the truck when it fired because it would knock so loud you would expect pistons and rods to fly out anytime, if they didn't. Of course, you would not be able to see any of this becasue the truck, your driveway, and half the neighborhood would covered with a HUGE cloud of white somoke from all the uncombusted slightly warm fuel pushed out the exhaust. Like, blot out the sun cloud of white.

The FD would be called. LMAO!
The smoke is an injector hanging, almost positive. I have seen it half dozen times and it always the same thing, bad injector. What you might have is just gummed up injectors if you have not been using additives. It is worth a shot to do an injector cleaning. Get yourself a can of SeaFoam, a quart of TWC3 2 stroke oil, a quart of Power Service, and a quart of Marvel Mystery Oil. Add the PS, 2 stroke oil, and MMO to the tank then fill it with good clean fuel. Drain the filter housing and fill it with the SeaFoam. Start the engine with the SeaFoam in the filter and let idle for 30-60 seconds. shut it off and let it sit for 24 hours.
Now go drive the tank out and see what happens. Unless you have a rod bearing starting to hang causing that hitch in the cold start driving it should not hurt it. If it does it is something that was close to happening anyway and ther eis no way short of a tear down to find that. My guess is a new starter and a thorough fuel system cleaning may fix your issue.
Good luck and post back any other questions or info you get.