that mushy foam is what is referred to as an emulsion. They are a pain, there are a few ways of dealing with them.

1.) Time, let it settle out on its own, they usually do,
2.) run the mess through a filter, with some sand in it,
3.) try breaking it up with a stir stick or rod,
4.) adding more solvent (water or NPS) and gently swirling it,
5.) adding salt will sometime help break an emulsion.

Emulsions are more likely when a two phase mixture has been shaken too much, or when the densities of the two phases are very close, but yours may have to do with the baking soda and vineagar. It should settle out eventually, but try adding some more water and gently swirling it.