I deleted iTunes again via the Terminal. Used the link you gave to download and install iTunes.
At first when I checked the iTunes version in Applications folder, I mentally groaned: it read 12.3.1. But when I actually went to iTunes and checked "About iTunes," the version was 12.3.0.44. (When I restarted the computer, the app read as 12.3.)
In general, it seems to work. Every action is about as fast as before the update. A few spinning balls, but mostly short-lived.
I tried videos, music videos, movies. Everything there seemed okay. But I ran across a new glitch with music files: when I play a song in the main list or in a play list, when the song is over, iTunes skips to a random song. Urg. Not as annoying as the spinning balls and freezes, but yet another issue to deal with that I did not have before all this started earlier this week.
This is the first iTunes update ever since the early days that caused iTunes to be virtually unusable. Certainly will think long and hard on future updates for iTunes; once burned, twice shy.