How do you get iTunes to alphabetize your custom playlist automatically?

You can change the sort order of the Playlist, providing that you have the Playlist in View as Playlist or View as Songs:

In the screenshot above, the view is View as Playlist and the sort order is Playlist Order, which means the order you added the songs to the list. As a consequence, songs are not in alphabetical order.

Select View/Sort By/Name (and make sure the Ascending line is ticked as well), as shown below:

and the view will now look like this:

Notice that songs songs are now in alphabetical order, following the convention of ignoring a leading "the" word and having the numbers after the letters.

To get that list on your iPod like that I think that in iTunes you have to right-click the Playlist and select Copy to Play Order from the pop-up menu. Then Sync iTunes with the device.

One thing though; I've experienced several occasions when a Sync appears to have been completed but many songs have not made it onto my iPod, even though they should have done. A further Sync (or even two) has been required in order to get my changes onto my iPod. It shouldn't be like that, but it is. (Perhaps it's been fixed in the iTunes update that I've downloaded this evening. That's iTunes 12.9.4.102).