Bill,
Although the paint was water based originally it was an emulsion which is simply bits of polymer suspended in water.
When it dries out the bits of polymer join together to form a plastic film.
Depending on which polymer is used this film will have varying levels of chemical resistance.
To soften it , water will achieve little but a solvent such as white spirit will dissolve it to an extent.
Try softening with a little white spirit , work in and then extract with hot water and detergent.
Cheers,
Doug