'62-'63 had a very accurate (if somewhat simplified) engine compartment with realistic shock towers, unusual for the era. The '62 promos had a simplified engine, but about 99% of the survivors are missing the air cleaner and hood.

For current build purposes, the '65 Fairlane Mod Stock chassis, when shorn of its vestigal wheelwells in the front should drop into the '62 annual body. The Mod Stock also has a good 260/289 that nicely proportioned and detailed and would serve a '62 well.

The '65 chassis' original exhaust system is removed (a race car, right?) so you will need to fab one... which leads to the next point... if you have a '69 Torino Cobra (or Mod Stock) that chassis is very similar to the '65, and is easily sectioned to the proper wheelbase and does not have the molded in exhaust. It has a dual system that would probably fit, or if you were going really stock, use half and fab a y-pipe.

I have not tried this, but, the Revell Thunderbolt has the vestigal single exhaust common to all Fairlanes that early racers were required to retain to pass tech, I will bet it could be cut and slipped into place.