I would attach it to something to keep it from shrinking. I've had grill cloth get very small on me after wetting it
Use a staple gun and attach it all around the perimeter to a piece of thin plywood before you get it wet. Then let it dry all the way before removing it. Use lots of staples.
Another way you can do this is to keep it in the console, remove the speakers and use a wet/dry vac and a spray bottle of warm water. Spray it on and extract as you go. I've removed lots of stains from many different surfaces this way by spraying with soapy solution first, then extracting with water.