There starts my confusion: "why can't I remove the user object from the workstation through the native tool?"
A basic identity management principle is that principals (users, groups, etc.) can only be added/changed/removed in the source directory. The UI for your Ubuntu system is designed to work with LOCAL user and group indentities, not for remote directory identities. This is analogous with you trying to delete a user from Active Directory using the Windows Computer Management console (it's designed to deal with local users and groups) - AD users can be changed with programs that interact with AD (ADSI) like Active Directory Users and Computers, adsiedit, AD PowerShell, etc.
Note this is the same for Windows, UNIX/Linux or OS X systems. When you delete the user in the Directory, there's no "magic" that removes traces of users in clients - because you may need to retrieve files from the user's home directory!!! Usually this requieres orchestration or a 3rd party tool, especially when it comes to client systems that are not always turned on.
I think this is the best answer I can give you in the topic.
Outside of this, is there a way to remove all traces of a user's login to the workstation (ex, their /home directory and username in the login screen)? Basically, if I wanted to "clean up" a machine before sending it off to a new user (without going through the hassle of re-installing the OS) or needed to fix some interface problem with an existing user of the workstation.
Yes. I stated this in my previous post. Remove the user's home directory. Provided the user did not write personal stuff elsewhere in the filesystem, you should be covered. Note that other operating systems have native tools (e.g. Windows has the System applet where you can delete user profiles; OS X has the Users System Preference, etc).
I'm hoping that when we get the full suite of tools running it will be easier.
Just to set the expectations clearly here. You have not asked in this thread anything directly-related to Centrify functionality, but normal operating system management. I am pretty sure that the Ubuntu ecosystem has tools that make these types of mundane tasks much easier. You can use DevOps solutions like Chef, Puppet, Ansible, etc; but that's outside of the scope of what Centrify does. Our focus is Identity and Access Management, more specifically Access Controls and Privilege Management.