You are now officially
by the Ford "hitching" plague!
This strange phenomenon has yet to be resolved... at least that I can find. It is weird how yours just started with a gear change though.
Try this: Disconnect your EGR hose going to the EGR valve, plug the vacuum end and see if this fixes the hitching drivability problem. You will eventually throw an SES code and the car will run slightly richer, but if the hitching problem goes away, you know that you are on the correct track. Because yours just started, you might have some hope. After diagnosing the problem, you can re-connect the EGR hose, disconnect the battery for a minute, reconnect it and the code will be gone.
I am still trying to figure out my own hitching problem. At this point it might even be a Kenne Bell problem. Ford has run every type of diagnostic possible and they came back clean. But they admit that there is a problem. Because I have a KB blower, they can not go any further. I have also replaced every EGR component, TB, IAC, MAF, DPFE, EGR Sensor, and performed a re-flash of the computer. A compression balance test was perfeormed and I and another mechanic independantly combed the car for exhaust and intake leaks. Every mechanic to work on the car has said that the chip from KB is the problem. KB has burned three chips so far. They are aware that I still have the problem and stated that they will work with me to resolve the issue. The part that is scary is the fact that neither I or any other mechanic can figure out for sure whose problem it "really" is. Ultimately I will probably have to get the car on a dyno and track it from there.
I have seen this problem posted on several boards and in each case there was never a resolution to the problem. The poster eventually "went away", never to be heard of again. I tried to contact those people to no avail. The problem is listed under several topics which include hitching, surging, missing, and bucking. My guess is that each person sold the car after giving up on the problem. There are several 03 GTs that posted with the problem, but there are some slightly older cars as well. One "key" common denominator may be the fact that all cars with this problem have "coil on plugs." I could be wrong about that, but most of these hitching issues have been with the newer Mustangs.
Good luck finding the problem. If you find the problem or give up on finding it, please post it here. It is very possible that your problem will be different since yours started with a gear change. My guess is that you had the probem right along and just noticed it because the gear ratio changed the rpm that you normally cruise at (during slower residential driving) and at that rpm the problem is more noticable. My problem becomes worse as the performance of my car goes up because (I think) the performance boost makes the car hitch more when it "recovers" from the miss.
I have also noted that mine hitches more at warmer temperatures. My guess for this is the fact that when the car is run in colder outdoor temperatures, it runs in open loop more. The EGR is not "supposed" to be active during open loop. However, I am not even convinced of that because I just fixed an EGR problem on my Chrysler Town and Country mini-van. On that car you can see the EGR pintle move in and out during throttle movement when it is first started at below freezing temperatures. That is how I diagnosed the EGR problem on that car; by pushing on the pintle at an idle. I sure wish my Mustang was that easy to fix.
I will also add that my Mustang pings a LOT more when it is colder outside. In other words, my pinging problem is inversely corelated with EGR hitching. Go figure.
I can not stress enough how bad a car can run with a bad EGR system. After I replaced the EGR valve on my Chrysler, it ran better than it has EVER run. It even shifts better. I almost traded the car in after trying unsuccesfully to get it fixed at the garage three times. I was fortunate to diagnose the problem myself and am VERY glad I kept the car. It now runs better than when it was new. I say this because I now know for a fact that a bad EGR system can wreck sever havoc. Because of this experience, I am guessing that either Ford or KB has not incorporated the EGR system well enough into the "total package."
These automotive computers are also STILL not sensitive enough to be able to tell us when a problem occurs. My minivan NEVER threw a code and that EGR was severely bad. And my Mustang is not throwing any codes as well. But I and the other mechanics know for a fact that there is a problem. Do not accept the common dealer comment "there is not a problem or there would be a code." Codes are only thrown for emmisssions and there has to be a "consistant" blatant problem for at least 40 miles SOLID before a code will be thrown. The computer does not throw codes for intermittant problems or non-emmision problems.
Let us know how you make out. It is very frustrating when people do not post how their problem ultimately got fixed. If I ever get mine fixed, I can assure everyone that I will post what the problem was, who found it, and who fixed it.
I guess not.
And then to say that it is all in your head! Sounds like when my wife kept getting sick with a pain in her lower back. A Urologist said that she had a mental problem and prescribed Valum. A general practitioner later found a huge kindney stone. 
Don't let them convince you that you are nuts buddy. I have a feeling that we may have to gather round to do a survey to get any kind of action on this problem. I will probably start something in a few weeks to start it off. Good luck and keep at it until there is a fix.
