Welcome to Just Answer,
Do you have a scanner?
Can you get me long and short term fuel trims while it is stuttering?
All of the work you have done I assume you checked all of the u-joints? I have seen u-joints bite people because they only check for looseness. I find it best to pull the driveshaft and make sure the joints aren't sticking.
I would not expect to see much change with the advance unless under an extreme load.
Did you change the flex plate when you changed the tranny, a warped or cracked flex plate will throw of the CKP signal.
Try a couple of things if you have not already:
1.)Power brake it through the RPM range and see if the stutter is there
2.)Try running in first or second gear and stick in that RPM range and see if it will stutter continously.
3.)Pop it in neutral while it is stuttering and see if it goes away.
Make sure it is RPM related and not speed or load related, it sounds like you are not sure because of the parts you have replaced.
Did you switch any parts to the transmission you replaced, was it used or reman?
A possibility it does not sound like you have looked into are the speed sensors, if one of them is bad it could cause some crazy shift or lock up problems.
I know I am asking a lot of questions, but I can't look at the truck myself so I have to rely on yor info. Bear with me and we will come up with something.
I know this might sound strange with all the work you have done, but have you had a compression test done. You are telling me it has a miss at idle, you may have a sticking valve or weak valvespring.
A vacuum guage can tell you a lot about the valve train with out having to pull all of the plugs and doing a compression test. With all the work done and no positive results I would go back over the basics.