Shaggy - reference photo courtesy of the NHRA providing history 1955 to 1964. Nice to see how dragsters improved with time in one picture. Using your 1960 to 1963 cutoff time frame, my guess for a correct drive closer to 1960 would be the use of a 3-speed standard transmission, using only 2nd and 3rd gears, 3rd being 1-to-1 ratio direct drive.
Myself, I have an early 1960s Speed Improvement dragster which I bought from the original owner builders from Altadena (aka: Poncho Beal, Mark Hopkins and Dave Hollingshead) who mostly raced at Lions. Speed Improvement was located in Long Beach and they advertised their dragster kit in the back of Hot Rod magazine. From memory, I think the kit as advertised was $199.00. Beal, Hopkins and Hollingshead used a modified 1955-57 Chevy manual 3-speed. The modification was the removal of the tail housing, shortening the output shaft, and making an aluminum plate to bolt in “to cover and seal up” the back of the transmission. A stock yoke with single u-joint was used to connect the modified transmission to the baby Olds rear; this area was covered with a metal shield. The simple handmade shift lever is connected near the back of the early Olds rear housing and uses a back and forth movement to control the 2nd to high gear shift. These three guys were into reducing weight, this dragster is 119” wb and weighs 900 lbs.
Back then with the shorter wheelbase, a thought process seen in many designs was moving the engine weight closer to the rear end. Today with a 225” wb, a different thought process rules.
What would I do to make it 1960-63 correct drive, select a manual 3-speed “you” like, modify it to work 2nd and high gear only, install it to meet your goal. Concurrently, I suggest you design your chassis for a shorty pg and shifter to fit in easily to replace the manual 3-speed. This provides you another drive option should you change your mind down the road (similar to what Calkins wrote, powerglides were available in 1963). If you don’t like pg automatics, another option taking more money is a modern Lenco CS4 2-speed, it’s the lightest and smallest and designed for 1800hp. Install the CS4 without a reverser, cover it with a vintage blanket in your chassis’s short wb and never look back. Alan