You're right about there being a few different connection styles.

As a starting point, it sounds like maybe you need to .....

Take the throttle connector off at the carburetor

Put the Morse shifter in neutral

Next, move the shifter to the Forward detent position (you'll feel a click, don't move it any farther)

Now go to the throttle cable and adjust the socket connector so it easily and smoothly slides over the ball and put it on. The adjustment could be done with the threaded socket or you might have to adjust the bracket itself since you had things apart and parts were mixed between a couple of engines.

Now, try shifting between Forward, Neutral and Reverse and see if it's smooth

Here's a picture of the typical throttle hookup on a PCM 351. It's a good picture, but the return spring is hooked up wrong and should be hooked up where the yellow arrows are pointing. The picture shows it right in the back but it should be at the bottom of the carburetor linkage as the front arrow shows so that it always wants to pull the butterflies in the closed direction> There can be variations on the spring mounting points but you always want that pull in the closed direction

You can also see in the picture, how the bracket can be adjusted or how the cable end can be adjusted at the threads.

https://ibb.co/tBZMPky" rel="nofollow">

Here's a picture of the bracket for the transmission shift cable. It mounts using the top left transmission to bellhousing bolt

https://ibb.co/jVBzwrJ" rel="nofollow">