Sorry! I missed this thread.

For the lazer cutting part, you can use blend-shapes, and/or composite 2 separate renders revealed by an alpha blend.

And if you are using Blobby Particles for your "molten-drips",
as long as its the same particle object you should be fine
because you can emit the same particle object from several emitters at the same time. That way you can have them interacting and forming one blobby surface.

Example:
When you make one emitter it comes with a particle object.
So you would make new emitters, delete their particle objects and then attach the original object to the other emitters so they blend with each other.

By deleting the particle objects you dont want, you can go to the dynamics relationship editor and make your favorite particle object be emitted form your emitters.

I think theres also an option under particles that lets you use "selected as emitter source" or something like that.
(not in front of Maya at the moment

Does that help at all?