Jay, my GTX was not the first FAST car in the 10's, that was Wayne Nelsons 68 ZL1 Corvette. My Hemi GTX was the first FAST Mopar in the 10's and the first FAST 4 speed car in the 10's.
I think a dual quad 67 Fairlane 427 would be one of the best FE powered choices. I would love to see a Cougar GTE running strong, but the Fairlane will probably have better weight distribution and of course the extra carb with open air filter is a big plus. A 1966 427 Fairlane might hit this roadblock: "The car year, make, model, body style and engine combination must all have been produced and available to the general public in the year claimed, in an actual car.”
One of my very favorite things about FAST is that it is REAL RACING with no break-outs, no index, no handicaps, no weights, no HP/LB rules, and you can never lose by going too fast. There is no attempt by the organization to create "parity". No classes, all run together. The better cars have an advantage, just like the day they were built, and they will not be punished for being better. But still, the stock tires are the great equalizer and there are many upsets and surprises, and the outcome of any given race is unpredictable. Driver skill is of paramount importance. The quickest 8 qualifiers go at it in a heads up pro ladder to determine the top eliminator. Qualifiers 9 and slower go into a best of 3 shootout with their closest qualifying competitor, so they all get a good, fun, close race.
That is why picking the right car is so important. Some stuff to consider when picking a car for FAST: Most of the factory bottlenecks must remain. Some are a deal killer. Correct heads- how much will they flow? Correct block - how many cubes and how durable will it be? Can the oiling system support high RPM without external modifications? What is the flow capability of the stock air filter assembly, the intake manifold, carb(s), exhaust manifolds? What is the potential weight and weight distribution? It is all important. But what ever car you choose, you will have an awesome time with great competition, lots of challenges, and one of the best bunch of racers you will meet.
Go for it, good luck!