landmass,
Here's a picture of my shifter:
the hat - Club Cobra Photo Gallery
The original 427s that Shelby put automatics in had this shifter - it's a contemporary Mustang unit from around '64-'66 I think - it has been a while. It does have the original appearance and is hooked to a C6, same as the originals. It is intended for a 3-speed auto and would work as is with a small block C6 or C4. Perhaps it could be used with an AOD but might need some tweaks?
As to cooling, I use mine on road courses and it is definitely needed there. Drag racing, I don't know - I would guess it depends on the number of runs you make and how soon after each one the next one happens. If you did one every 10-30 seconds like the road courses require, you'd definitely need a cooler. If there's a half hour or so between runs, probably a cooler isn't needed. After incinerating three transmissions I tend to think a cooler is necessary even for spirited street use. Most street vehicles come with some kind of cooler built into the radiator tank at the least. Owners add them if the vehicle is used for towing and doesn't come with a tow package. They are relatively cheap especially when compared with renewing the trans and converter.
As far as shifting, I put mine in D and go racing. It doesn't upset the car if it downshifts under power - something that seldom occurs. If I'm exiting a really slow corner, the downshift happens at part throttle so it doesn't try to break the rear tires loose. With lots of HP, one gets an education quickly about the meaning of the term "roll on the throttle." If you stomp it you'd need to take a compass reading first so you might have some idea where the snap spin is taking you...
The trans builder can probably take care of the downshift behavior. In drag racing, get a trans brake and see how far you can carry the front tires when you stomp it
As far as the upshift behavior is concerned, mine (and likely most others) behaves like a street car: The upshift speed can vary with throttle position, so if you accelerate gently it will upshift at low speeds. As you increase throttle and load, the upshifts move to higher speeds.
Some of the shift point behavior is adjustable with the "kickdown" lever and linkage found on the C4/C6 - the AOD can be adjusted too I think but I have forgotten how. Sorry. I dimly recall a TV (throttle valve) rod for the earlier all-mechanical version of the AOD - the caveat there was that if you adjusted it incorrectly you were likely privileged to buy another trans.
Whatever you decide, have fun with it!
Tom