You have to install a clear hose on the return from the injection pump to eliminate any possibility of air intrusion when hot.

I would but others will disagree probably. Engine at operating temperature. Unplug the glow plug harness and read the milli volts the glow plugs are producing. From each contact in the harness to the engine itself as ground

Do not use the negative battery terminal. It may not be accurate at first as the glow plugs are not newish from the same batch.

Yet if there is a glaring error. Just interchange two glow plugs and read the voltages again. If voltages are really clean I suspect air intrusion. If not the injection pump.Actually this could be further simplified by reading the voltages with the engine cold. Then hot with the poor idle. Each voltage you have recorded should change in the exact same way.

I seldom get into the milli volt testing. As the use of it requires quite a bit of thought. Perhaps it is just me with my background. I just consider it a tool. Crude perhaps but it does indicate a temperature present in each cylinder. If they are not very simular you have a power balance issue. The problem with people using it is the shortcuts they take.

Another possible test is start the car and as it warms up keep a light spray of water on the injection pump to hopefully keep it colder. If the idle does not deteriorate as the car gets up into the problematic temperature range. It would have to be the injection pump.

I try to stay away from suggesting people use the milli volt method. Yet yours is a painful enough situation to try it.

Personally I would like to examine the two sets of readings you aquire. I do like elimination the EGR circuit first as well. If nothing can be indicated as an issue with the double milli volt test. I might think about checking the top dead center of that engine. In the milli volt testing I look for indications of all sorts of problems.

My suggestions such as they are have to be preceeded by the absolute verification of no air ingress is there when the engine is at operating temperatures.

There obviously was something going on very early in that engines history for someone to touch the injection pump adjustments.

Thank you again everyone for all of the help.

We pulled vacuum on the EGR valve while the engine was running and up to temperature, and there was absolutely no change in how the engine ran. The techs think that the EGR valve itself is stuck slightly open. They are going to remove the EGR assembly and see what's going on.

Doubt it will make any difference. These things will easily run even without the intake manifold. This is not a gas engine.

These are both worth a try and are easy. It does sound like air intrusion is a possibility. A clear hose may spot something.

I also doubt egr. My car idles fine with the egr open or closed.

But I have a question. If there was air intrusion into the fuel system, wouldn't that manifest whether cold OR hot? In other words, it would have a rough idle all of the time?

No need to remove the EGR system. Just plug the rubber lines with a golf tee. That way you can go back to factory set up if there is no difference. As a purist I always like to see factory set up.

My issue was odd. I got an air leak at the Plastic Fuel Filter.

I had the clamp down really tight but the hose was old and in-elastic. My guess is that when it got hot under the hood the plastic filter got more flexible and warped and leaked air.

Replacing both sections of fuel inlet hose fixed it.

How long were you trouble shooting this?

I’d have thought you’d have replaced all the fuel hose as a matter of course.

Well it’s just a theory. A crack or loose seal can open up as the plumbing or a seal heats up. It can contract when cold. Or maybe a hose gets just a tad softer or more compliant hot and doesn’t seal around a nipple in the fuel system but tightens up when cold.

This is a wild guess. A clear hose may accumulate some air which would indicate a small leak. Im sure you’ve checked all this easy stuff.

Whatever is wrong with your car will be interesting to hear about. Please follow up when you solve it. It sounds like a tough problem.

For weneversleep:

Under load (higher revs) air can be pulled in through a marginal seal on the suction side (aft) of the lift pump.
Observe the inlet line to the secondary fuel filter for rapidly moving air bubbles when you blip the throttle to race the engine.

If the clear line is no longer translucent due to age, use a flashlight placed adjacent to the darkened line.
If you see air bubbles, you have air incursion from a leak aft of the lift pump and/or from cavitation.

The buildup of air bubbles in the high pressure circuit of the IP (as the engine runs) may eventualy affect the hot idle smoothness.
The next day, on a cold engine, you can have a a fairly smooth idle intitially, as the accumulated air in the high pressure circuit of the IP
can purge faster than any new additional air incursion (at cold idle).

When I got the Car I only replaced the Radiator Hoses. I have worked on a lot of Diesel Engines and have never found an air leak issue that happens in this manner. However, however most diesels don't use the plastic filters.

I had done a whole list of things to reduce the shaking to normal. I did not actually trouble shoot the issue. It just happens that when the hood is open I look at the plastic filter sometimes for evidence of stuff growing in the Fuel. Usually with the engine not running.

One time I checked with the engine running and hot and I saw an occasional bubble moving along. I checked the clamps and they were tight.

When I checked another time right after start up the engine cold and looked I saw no bubbles at all.

When I took the filter off I found out how hoarded the hose was. Also that was not one that had the metal nipples on it. The housing was all plastic.
With the new hoses there was no more bubbles.

The Plastic Lines from the Spin-on Filter Housing to the Fuel Injection Pump were too dark to see some random bubble.

For most people the air leak issue is the hand primer. But, the previous owner had replaced the one on mine with the newer style hand primer.

I've collapsed the sleeves on those cheap plastic units by trying to get the hose to stop slipping. Now, the metal sleeved pre-filter is the only one I buy.

I have had no issues with my plastic ones and I am using US sized hose.

You might have tried this but what are your 'hot' engine temps? Make sure you have an 80c thermostat. Lots of times they get replaced with cooler temp thermostats that don't get the engine hot enough to around 90c normal operating temps.
Also you probably already know this but how rough are we talking here? All of the 300D's I've seen run a little stronger when they warm up giving the appearance of being rough when its the way normal diesels operate.
Lastly it sounds like this car needs to be driven! Put some miles on it, you may find that things improve considerably :)

Thank you again to everyone for the continued help. I have an update, and this time it's good news!

@Alec300SD suggested that the fuel hoses on the intake side of the pump might be degraded, causing air incursion. Well, the tech took those rubber lines off, and they were falling apart inside. Maybe there was air incursion, certainly there was a choking-off of full fuel pressure.

Replaced those lines as well as the rubber line for return, and the majority of the shaking is now gone. The engine still shakes a bit at idle, but nowhere near what it did before. And, most importantly, sitting in the driver's seat, there is no shaking felt.

The car has always been a bit sluggish as well. I took advice from another thread and replaced the throttle linkage bushing assembly (at the firewall). (unfortunately, for an 84, this part is not available new anymore, but I took one off of another car as a test, and ordered the bushing insert from the seller on eBay to rebuild the bad one) Now, the throttle response is as it should be, engine is getting full power, and life is good!

I think the next steps are to replace the clear plastic fuel lines (which have turned brown); those have been ordered, and maybe that will make things even better. And to now drive the heck out of the car; I'm sure there was quite a bit of carbon buildup in the intake and cylinders resulting from the mis-calibrated pump that needs to be blown out.

Anyway, thank you to everyone again for all of the input, and I will continue to update this thread as I drive the car!