I think I figured it out. Using ADSI Edit you can look at properties on an object (e.g., a user), but by default it was filtering out "constructed" attributes. Using the Filter button at the bottom right of the properties screen I was able to show these additional attributes.
The "msDS-PrincipalName" appears to have "[netbios domain name]\[sAMAccountName]" as its value.
If I go into AD Users and Computers and change the "User logon name" from "email@example.com" to "firstname.lastname@example.org" this affects the "userPrincipalName" attribute, but not the "msDS-PrincipalName" attribute. This is good in my case, because my other system (SharePoint) does not recognize this change either.
If I go into AD Users and Computers and change the "User logon name (pre-Windows 2000)" from "KIRKDEV\gwashington" to "KIRKDEV\g2washington" (note, that I cannot change the first part) this does not affect the "userPrincipalName" attribute, but does affect the "msDS-PrincipalName" attribute. This is exactly what I want because my other system (SharePoint) does recognize this change.
Side Note: I said SharePoint does recognize the change, but that is only if the user has never logged into that SharePoint site collection before. Once the user has logged into the SharePoint site collection, the tp_Login field in the UserInfo table is set with the "msDS-PrincipalName" value and that does not seem to change. So, I may have to find a way to force that to be changed or just say that this scenario is not supported.