You are making this hard.
The block is the same. The mounting ears and bellhousing pattern and dowels are the same. The starter area is the same. The accessories all bolt on the same. The rear main seal retainer is different at the side seals, but you can use the common seal retainer in the older blocks. The freeze plugs in block and head are a different type 1962 and older, but it doesn’t change anything. They are a disc instead of a cup type.
Spend some time troubleshooting the 361 and see if you can fix it First.
I am not trying to make it hard but rather make sure the OP knows what he is getting into and learn a bit myself
Myself, I'd go with the poorboys suggestion and upgrade to the aluminum 727. I had issues a few yers back finding a turque converter for a 59.The first one was DOA, the 2nd had the wrong ring gear (industrial unit) Lost my backsider on that deal. Working around the issues associated with the 727 seem to be a bit less challenging and one gets a more reliable trans. Or as you stated, see if the 361 can be fixed with minimal cost / effort
