So taking that all into consideration, I took some needle nose pliers and
slightly tweaked the metal pin that was misaligned with the hole in the
carousel. Now it fits just fine when the cam elevates the play mechanism
into position.

I say -- without sarcasm -- that it's gratifying when common sense works.
(It so rarely does when servicing electronic equipment.)

The reason this wasn't solved sooner was that there was no obvious /reason/
why the pin should have been misaligned in the first place. How /could/ it
have gotten misaligned?

I had a similar problem 40 years ago. I pulled out my Nikon F and discovered
the film advance was jammed. It turned out the take-up hub had been BENT at
the middle, as if someone had banged it with a mallet. How did it happen? I
never learned.