A 301 was a short-stroke 318; put differently, it was in essence a 318 with 277 crank.

All pre-62 (i.e., 61 and earlier) Mopar V-8's had an extended crank flange that the torque converter bolted directly to (no flex plate). So, a 64 318 won't bolt directly to the 57 trans without some kind of adaptor.

If you can locate a factory 57-8 Plymouth 3-speed pushbutton control (they are around), a 62-64 Chrysler pushbutton shift cable will work on your 64 trans and is long enough for your car (a B-body cable will probably be too short). In fact, I'm pretty sure the 62-4 Chrysler cable would work with the 2-speed pushbutton setup and the 64 trans except you won't be able to manually shift to low. Of course, with the 64 trans, you'll need to rig up some kind of park lever setup whether you run a pushbutton cable or convert to floor shift, as the 64 trannies used a separate cable for park, and 57 Mopars automatics didn't have a park.

You won't have an emergency brake with the 64 trans unless you swap to a later rear that has the emergency brakes inside the rear brake drums or convert to a 62 Chrysler trans-mounted emergency brake setup.

I'm using a 62 Chrysler torqueflite in my 59 Dodge because it has a drum-type emergency brake on the rear of the trans like all the (61 and earlier) cast-iron torqueflites and all Powerflites, but my 59 has a big block. I don't think there was a small block (62-up) aluminum torqueflite that had the trans-mounted emergency brake. However, if you want to go to the trouble, and your 64 trans is a 727 (and it should be), all the parts to convert to a trans-mounted emergency brake can be swapped in from a 62 Chrysler trans. If you do this, you will have to use your original 57 backing plate on the emergency brake, as the 62-up cars used a foot-operated emergency brake and the earlier cars used a hand-pull under-dash emergency brake, and the cables for each type of setup don't interchange. Use the 57 backing plate, and your stock 57 emergency brake cable will work on the 62 Chrysler-type emergency brake setup.

Transmission mounting positions vary, but I think you'll find that the mount holes of the 64 trans will end up an inch or two in front of your 57 trans crossmember. On my 59, I cut off the bracket from a 64 crossmember and welded it to the front of my 59 crossmember. Used a stock 64 trans mount; lined up perfectly.

I used 59 Chrysler big block engine mounts/brackets on my 59, which bolted right up to my 64 413 block. I'm pretty sure your factory 301 engine mounts/brackets will bolt to a 64 318.

Now if this all sounds like too much work, a 61 or earlier 318 will swap right in and bolt to your original trans with no modifications.