Changing default shortcuts from Shift-Command-Z to Command-Y; Unexpected behavior!

I want to change the shortcut Shift-Command-Z to Command-Y, however, I could not find any way to do this universally.

I did however try changing it for a specific app to see if that would work. But the weirdest behavior happened;

Changing the setting:

Now in the Notes app, it first appears that it did work (Notice the Redo shortcut has changed to Command-Y):

Then testing, by typing something, still okay:

Then, deleting something, still okay:

And here is the weird part. Now, I hit Command-Z to "Undo", and suddenly, the "Redo" shortcut has changed from Command-Y to...Command-Z; and now both Undo and Redo are Command-Z:

Can someone explain what is going on here? Did I write the shortcut wrong? Is there a solution?

Also, if anyone can give some insight on how to universally change default shortcuts throughout the system, such as Shift-Command-Z to Command-Y, instead of going through and changing the shortcuts individually for each app, that would be appreciated. I understand the reasoning behind adding the Shift, but I like it shorter, and my old Mac I just upgraded from did this just fine.

Thank you!