David,
Here is my experience with switching to synthetic. This is on a few different engines, not all diesel.
The first one I switched to full synthetic was my 03 6.0 Excursion. One of the best "upgrades" I've done to the truck. Starts easier, runs better, and it doesn't use any oil, didn't with conventional. It's at ~171,000 and just now had my first injector issue... still has all 8 factory injectors and the factory HPOP. Also factory turbo and head gaskets. So 15 years and 171,000+ miles with no issues, I believe running the better oil (Chevron Delo 5W-40 Full Synthetic) and good filters, changing at 5,000 miles has helped reach this.
The second was my 91 Jetta IDI. It was switched because I had the oil for the 6.0. To use the same oil in both and change the oil, I only needed to buy one extra gallon. The 6.0 holds 15 quarts, the Jetta 5. It had right at 300,000 on it when I switched. Oil consumption didn't change between conventional and synthetic, about a quart per oil change cycle. Was still running synthetic when I sold it.
I also switched my 2 single cylinder Kohler air cooled engines (14 an 16 HP). I had been using Motorcraft 15w-40 Diesel Oil (left over from the 6.0) and they seemed to like it. They call for Straight 30 weight. When I did my spring oil change, I used the Chevron Delo 5w-40 since I had some on hand. These DID NOT seem to like that oil. I mowed once, noticed increased consumption, and noticed at lower throttle levels, when I had the headlights on, it would haze blue (burning oil). I switched both back to Motorcraft 15w-40 Diesel Oil and they went back to normal. One hadn't been ran, I switched it where it sat. I now have gone back to Straight 30 Weight, that, or the conventional diesel oil seems to work better.
I also switched my 2000 P71 Crown Vic to the Castrol High Mileage Synthetic Blend oil. Corey
@Dieselcrawler recommended it, for the Ford "mod motors" to help in oil consumption and burning oil. I switched it and consumption when down (it still consumed oil, but not as much), and the smoke out the exhaust completely quit. Because of this, I have run this oil in my 07 P71 and the Infinity QX65 (5.6L V8). They both seem to like this oil.
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I'd say go for it. But don't expect a drastic changes. With the condition of your engine, you should be good, and it may help to prolong the life. I would not go super long on the OIC, but you might be able to stretch it out a bit. I still change the 6.0 at the recommend 5000 miles interval, because of the shearing the 6.0 Injectors cause of the oil. I even keep the gasses at the 3-5000 mile interval. I keep my vehicle for a long time... so changing the oil a bit more often is cheaper in the long run (at least in my opinion, I can afford a few buck more in oil than a sever thousand dollar rebuild).
Now, for the 7.3 IDI I have now, it leaks enough, that I'm going to stick with conventional. Right now I have a case of Mobil Delvac 15w-40 because it was on sale at Sam's Club ($34 a case). I'm going to change the rocker cover gaskets, and see what else might leak. This truck isn't planned to be a daily driver, or a complete restoration. So as I make improvements, it may get switched over to synthetic, but right now, it will stick with conventional, since changing the oil every 3000 miles won't be that often.
I like synthetics, but would say try them, see how YOUR engine responds to it. It may like it, it might not. I've seen both in different applications, and have made adjustments accordingly.