That is a ton of work for some big uncertain if's. You should use the entire 62 drivetrain engine and transmission. Look into Imperial Services for advice on getting a custom transmission cable to do your swap. I wouldn't swap internal engine parts swaps without having a competent machine shop doing so.. it's far easier taking the newer drivetrain and putting that in entirely.
https://www.imperialservices.net/
I agree , if the cast iron Tflite hard parts are okay and can be repaired with a regular master overhaul kit and bands , that’s what I’ll do to keep it all original . If not , and I have to pull the engine , I might as well just bite the bullet and have the unknown parts car 62 engine checked , if it’s usable , I’ll have the short block redone , and fresh valve job done on the 62 heads , if the 62 heads are bad , I’ll use the known good heads from the 60 413. Hopefully , the cast iron Tflite just needs a regular overhaul , problem solved I’ll use it and no engine removal will be necessary . That will be the fastest and least expensive way, far easier and quicker than swapping cranks or engines
If I’m going to have to pull the engine though , I might as well end up with both a freshened up 62 engine and use the overhauled 62 aluminum Tflite transmission in the car together . I can save a bit by assembling the prepped block and heads myself , and prefer to do that anyway to know everything was done correctly.
No transmission cable adapters would be needed , both the 60 cast iron and 62 aluminum Torqueflites use the same shift cable connected to the pushbuttons , and both have the same foot operated cable to the drum parking brake , neither of the 60 or 62 Tflites has a Park pawl .
The 63 up Tflites added a separate Park lever on the dash to operate a cable operated Park Pawl mechanism on the tail shaft, and used the same shift cable from the pushbuttons to the transmission . The 63 up models used cable operated rear drum park brakes The pushbutton 64 T Flite in my Rat wrecker coupled to its 54 Dodge 241 Hemi has that set up , a Park lever on the Valiant control panel to operate the cable to the Park pawl , and the shift cable connected to the pushbuttons to select the gear desired . I used a diff mounted mechanical disk park brake on my rat that works well.