Hi Christopher,
I can't help but think your client has inadvertently gotten their security preferences backward. Microsoft is aggressively trying to kill off Basic authentication for O365 as it's incredibly insecure compared to Modern auth (OAuth). So much so they're proactively disabling Basic auth in tenants they detect aren't using it on behalf of customers. I've heard dozens of requests to move from Basic auth to OAuth and this is the first time I've ever heard it the other way.
See: Microsoft - Exchange Online depreciating Basic Authentication
Modern vs. Basic Authentication: Hopefully by now we don’t need to expand upon the virtues of Modern Authentication. Enabled by default for all new tenants since August 1, 2017, Modern Auth is the superior alternative for all users and applications connecting to Office 365. If you haven’t turned Modern Authentication on yet we certainly recommend it.
If you have OAuth working, I'm not aware of a legitimate security case for switching back to using a method that Microsoft is actively working to depreciate because it's insecure.
In short, I'd really sanity check that's what they want and why before spending any further time troubleshooting an auth method that's liable to be forcibly disabled in a year.