To answer your last question: Yes 64 Series 62 was built with the hydramatic transmission.
I believe the S//N# of the engine will indicate the the year/size but don't know have the decoder ring for that. It's probably somewhere in the help tab too.
If there was a turbo 400 trans behind the 429 engine the hydromatic cannot be mated to it without changing the crank shaft in the engine —-or the flywheel will be breaking
No all 429s. came with the turbo 400 trans In 64 as some models in 64 came with the Hydromatic trans behind it
Those 429 engines with the Hydromatic behind them in 64 would have the correct crankshaft in its engine to bolt up to that 429
So it can happen that way
Measuring the back of the crankshaft - if that is possible —will tell you which crankshaft you have in the engine
There is only 1/8 difference in the diameter of the end of the engines crankshafts
That is why the crankshaft will break
I would think engine numbers could get you back to the engine in the car origins ( were it started it life )
I do think others on the site could help find the engine info you are looking for it you post the engine numbers on this thread
Great references to Jason’s info on the subject
I posted before I opened your info