The pumps with plungers are replaceable as you noted. Usual procedure is if the plunger isn't stuck and it doesn't leak excessively it is probably good. There is an outlet check valve that might be bad but I don't know how you would know unless you have a bad injector that is allowing compression from the cylinder to go back up the injector line and put air into the fuel gallery of the pump as the engine runs.
The lifters should be pretty simple to inspect and determine if they need anything. Camshaft should probably be checked with a dial indicator to ascertain the correct lift unless it shows obvious spalling of the lobes. Really nothing too technically demanding about one. Final check is to set the lifters using a depth mic once the pump is back on the engine. Probably could use the same depth mic to check the Camshaft lift.
Since the oil in the sump is not pumped or splashed around during operation I doubt any great harm was done by crud that ended up settled in the bottom. Better for it not to have ever been in there but less harm than in an engine crankcase etc. I would just clean it out, check for any sticking pumps and then run the engine to determine what if anything is going wrong. As I said, setting the lifters is best done on the engine to account for any wear in the gears between crankshaft and accessory shaft that drives the injection pumps. The only thing to watch out for is that the flywheel with the TDC marks you use while setting the lifters can be installed wrong. It is important that you watch to see that each lifter you set is rising as you reach TDC and continues to rise as the engine is turned past TDC to go on to the next cylinder TDC mark. If this is not the case you may have not been on compression stroke (turn engine one complete revolution) or the flywheel is installed wrong.
Doesn't Bill Walters, a member here, still work on them? He did a great job on my fuel injection pumps. Not sure if he works on the whole unit.
Install the injector lines to the pumps but pointing out over the track. Screw injector adapters on the lines and tighten. Turn engine over to purge air from the lines. Then screw the capsule injection "valves" as CAT calls them on the adapter thread. Note......you cannot tighten more than snug since the threads do not fit tight. If everything is clean, they will not leak much. Now turn engine over with throttle open and watch spray pattern from the injectors. The injectors should open at about 425 psi minimum. If they spray you know the pumps are capable of that at least.
I think is is possible to get the symptoms you describe because the rack is stuck in fuel shutoff position. Open the side of the injection pump housing and watch rack as you move throttle control from shutoff (push up/forward hard on lever in operators station) to full throttle (pull back/down on the throttle lever). You wouldn't be the first to have one stuck in shutoff. This is preferable to being stuck at full fuel! Sometimes all it takes is a hard snatch on the lever to pop the governor over the internal shutoff detent to the fuel on position. In the fuel on position you should be able to easily slide the rack front to back in the fuel pump housing.
You should be able to rebuilt it your self if you can find parts. It is very bad practice to test injection pressure with your finger, the high pressure fuel will blow your skin apart and take months to heal if you don't get infection and lose the finger....WA7OPY
Yes, the pumps will allow fuel to flow through and even make it spurt as the plunger moves up, but not build up pressure when the rack is in the cutoff position. The injector valves keep low pressure fuel from flowing to the cylinders.
Remove the cover on the side of the injection pump housing and watch the rack move to front for fuel on and rear for fuel off. The idle stop assembly in the governor has a spring loaded detent that holds the rack to the rear for fuel cutoff. With time and slop in the linkage between lever and governor you can move the lever a lot and still not get the governor to flip the idle stop and let the rack move forward. I suppose it is possible the rack is bound up in the bushings in front and rear of the cast iron housing but usually the problem is a stuck pump plunger. If the plunger won't move back down after the cam pushes it up, it sure wont twist and it locks the rack up. Any plunger that is stuck up should be sprayed with penetrating oil and pried up and down with a screwdriver etc if possible. Once it moves up and down freely it should also turn freely so the governor can move the rack smoothly.
When the governor is not in the stop position, the rack should move easily fore and aft with just fingertip pressure. You should feel some spring pressure as you move the rack toward the rear as the governor spring wants to pull it forward to increase rpm (engine is stopped so the governor is set to increase rpm).
If you cannot get one loose, its time to remove that pump and replace. The pumps are precision machined and each plunger is honed to match the pump so there is no tolerance for gum or solid particulates in between. The gear quadrant that is attached to the bottom of each plunger to engage with the rack is set to calibrate the fuel delivery rate so it is safest to not pry the rack front to back attempting to free up a stuck plunger.