1961 and older was a cast iron torqueflight or a powerflite 2 speed depending on the car.
1962 was the first aluminum 727 with a 6 bolt crank and a flexplate.

The 1961 and older crank has 8 holes and the flange sticks out much further.

In the 59 dodge, the generator mounts on the exhaust manifold
and water pump housing. There are no bolt holes in the ends of the heads.
The power steering pump mounts to the water pump housing.
So other than the crankshaft and water pump housing you could use the rest of the 68 383.

Last year of a 361 in a car was 1966
Last year of a 413 in a car was 1965

Is the engine to trans bolt pattern the same?

That's why I'm saying, build up the 383 with the 361 crank. ( and well... WP and exhaust )

I'll ask again, Is the engine to trans bolt pattern the same?
Also are there any other dimensional differences beyond the length of the crank ? motor mounts? Sounds like a can of worms to me

I believe the bell housing bolt pattern between the 59 361 and the 68 383 are the same, Chrysler was pretty consistent concerning bell bolt patterns.

As far as the rest of the stuff? Most of the guys that did such swaps are no longer around, or couldn't remember for sure. The crankshaft issue would have been the end of the swap for most guys. I'll go out on a limb here and say the 361 motor mount brackets will probably bolt onto the 383. You will have to use the 59 body end of the mounts in the 59 car, that I'm sure of, unless you want to do a lot of redesigning.

If you really want that 383 in that car, do whatever it takes to put the 383 trans in the car as well. Its going to be easier to manage shift operation and deal with emergency brakes then it will be to deal with crankshafts, and the 383 trans would be a better trans. Gene

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.

The mounts are the least of the problems. They will interchange from block to block. If you are looking to keep that transmission and go to a bigger motor then forget about the newer 383 and get one from a 1959 to 1961 Mopar. You could even use a 413. If you get an older 383 just beware because they made it in a low block and a raised block version. I believe the 59 and 60 Windsor used an RB 383. The low block version you could use you parts from the 361 on.

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

the newer 383 has a 6 bolt crank flange, while the older 361 has an 8 bolt crank flange, and as has been already stated, the 361 crank flange is 1" longer than the newer 383.
so if using the 383, some kind of an adapter will have to be made to mate the crank to the 361 flexplate. that may, or may not be hard to do. it may not be even possible, i don't have a crank in front of me to inspect as to the possibility of such an adapter.
the 59 engine mounts will have to be used on the 383, as they are an entirely different style of mount than the newer 383 uses.
the accessory mounting holes on the end[s] of the 383 head[s] may be different than the 361 heads. i'm just stating this as a precaution if the OP decides to use the 383 heads to get the 361 running. also, the 361 heads may be closed chamber heads as well, while the 383 may have open chamber heads. [i don't remember what the 361 had for heads.]
i think this post may be repeating myself.

The mounts on the 361 will work on the newer 383. I used them to put my 440 in my car. I think he is looking to try and stay somewhat original and wants to keep the pushbuttons. There are adapters made.