Thought I'd add my 3.0 cam synchro experiences...
My 2002 3.0L has been in my family from new. I bought it off my parents in 2008 with 49K miles to replace my rusted out Explorer Sport. My parents always had the oil changed at the Ford dealer with bulk 5W20. I used Pennzoil yellow bottle conventional 5W20 and 5W30 after that.
At 61K miles the original synchro failed. I was familiar with the problem ahead of time, so when I started the truck up on a cold morning and heard "SCCREEEECHH...chirp chirp chirp chirp" I had a pretty good idea of what was up. I was living in an apartment and had no convenient place to work on the truck, so I took it to a Ford dealer and they replaced the synchro and sensor.
In the next 85K miles, the truck saw some hard use (lots of towing and heavy payloads), and I switched it to synthetic oil. Mostly Mobil 1 0W30. Figured a 0W would get the synchro oiled quicker at start up. The second synchro did last 24K miles over the original one.
At 146K miles, the truck started bucking when first started before it was warmed up. Spark would just cut out when taking off from a light. Happened once or twice for a few seconds, then was real bad one morning on the way to work. No noise this time, but again I had a gut feeling about what was happening. I got a new Motorcraft synchro and put it in myself by marking the intake. Before putting the new synchro in, I soaked it in clean motor oil and let it sit for a while to make sure the inside of the assembly was completely oiled. When turning the old synchro, it felt rough, whereas the new one was completely smooth when turned. We'll see how long this one lasts. It has a little over 22K miles on it now, so it's too early to tell.
It's an annoying problem, but if you catch it early and deal with it at the first symptoms, it won't be a big issue. Shops tend to charge a lot to replace it, but it's really not a bad DIY repair except for the location at the back of the engine.
I think poor lubrication is the source of the problem. Both times it failed in my truck, symptoms were noticeable on a cold start with outside temps below 40*F.
Personally, I stick to Motorcraft synchros. Dorman ones apparently don't have a good track record. A1 Cardone remans might be okay. I wish there was an improved replacement that just didn't go bad though. It's basically a consumable part on these engines.