You may want to start with something alcohol based.  Sounds like that is what got this all started 
 
 Isopropyl, 
Or something with alcohol in it.  Hand sanitizer will be more gel-like so stay where you put it. 
Try a small area. 
I'd mask off the area and only do the paint with an acid brush or q-tips
Lay it with HONDA flat so you are not fighting gravity.
There are other paint removers for fabric at your local fabric store too.  
Then a host of 

 ones from Orange strip to Toluene etc, but more risky to do damage to the fabric without testing what you have. 
Alt