I have a resolution to this.
First, I should mention the production server is run by the IT department, in the server farm. In the original question above, I stated "I simply change the user/password credentials on the service, and restart Apache." Actually, IT changed the password and restarted Apache. This is a semantic difference, but one which turns out to be important here.
This morning, I asked the people over in IT if they had any ideas on the problem. The sysadmin poked around, and realized he hadn't actually changed the user password at all, despite his insistence that he had done so.
I'm not going to throw IT under the bus here. They're busy people, and they are human, and that's okay. But I will offer this resolution to future developers: If you encounter this kind of problem I suggest "re-updating" the password, because maybe it didn't happen right the first time. Maybe he updated the password on a different service (which also needed it anyway). Maybe he typed it in, mistyped one character, didn't read the failure message, and closed the window. Whatever, it's not important.
The resolution is to update the password in the service.
Cheers!