Are non-degree courses a viable option to offset a low master's GPA?
This wouldn't hurt, but whether it helps depends on the admission process at that university and how competitive it is generally.
Another possible benefit is that the faculty (at least a few of them) will become familiar with your work. It also shows some seriousness of purpose.
The letter of recommendation may be possible.
But, have you explored the option of just applying. You may be making assumptions about how important your GPA is in the process. Many things are considered, including letters you might already be able to get and how strong your background is generally, and even undergraduate work.
If you can discuss your current situation with someone at the university, do so before you make decision.