What is a 361 big Block ?

You are ok with a 62.The 727 TorqueFlite was well into use by 62.
That is if it's application was automotive and not industrial that the 361 was used for.
I have a 63 361 that I'm building now.Crank/rods are the same as the 383.
Major problem is standard bore pistons that are out of the box ready are few and are low compression. But if you have the four barrel version( you stated it was) and it is not frozen/locked up you may have a good starting point.A 361 and 383 performance is almost identical.A 284/484 Purple Mopar cam is a good one.I used to run the Mopar Purple 509 in many engines in the past.