Update:

As shown in the above image, I've been able to figure out how to make emited particles stay on the plane of the image and spread downward by making particle goal is the surface from which they are emitted. Unfortunately, the particles are clumping on the floor at the base of the painting. I would appreciate help making the particles to spread about the base of the painting once they reach the floor.
I still don't know how to merge or convert the particles into a smooth surface for rendering. This smooth surface should retain the colors of the various particles.
I've uploaded the scene shown in the above screenshot, including the image that I'm trying to melt, as a zip file to:
http://proceduralcg.com/wip/Scene.zip
Thanks.