That was one of the first things that I tried during troubleshooting, but it turns out, it was an issue within the database.
I took a closer look through the ost_user_account table and found 2 entries for each of the 6 affected users, 1 entry showing the username as their expected (just username) and the other username as their email address. For each of these, the user_id number was the same for both usernames, which I found was odd. After closer examination, I found a few non-affected users who also had 2 entries (as previously described), but the user_id was different.
In the Staff/Agent Panel, I took a look at the User Directory and noticed that for all users with the duplicate user_id, if I clicked on their names, I would get the HTTP 500 error. In addition, if I would just hover on their name, the preview window was blank; it would not show the user or notes information.
As a test, I deleted the id (not user_id) with the oldest timestamp for the non-working users. Once I did this, everything was fixed and the users were able to log in to create tickets. The majority of these users are also Agents, but they did not have any issues logging into that Staff panel.