Way to think outside the box!
To add a few pointers to your process... use as little moisture as possible when cleaning the headliner to prevent "wicking" embedded dirt back to the surface and leaving the dreaded water-ring mark. This is especially true the older a vehicle is because more dirt/dust has had a chance to get into the fabric.
Also, using a microfiber towel and a fan to dry the area as quickly as possible will minimize wicking.
When agitating the stain, use as little pressure as needed to get the job done to prevent fraying the fabric threads.
Lastly, if you're wanting to use a legit interior cleaner product that is specifically made for car interior fabrics, consider Opti-Coat's Fabric Clean and Protect. This product is amazing, especially on lighter fabrics, and is outstanding at removing water marks without the common wicking problem.