Is it possible to combine vertex colours and a texture into a new texture?

Request advice on a direct, specific point:

Is it possible in Blender to produce an image that blends the vertex colours of an object together with a texture, e.g. through some method of baking I cannot work out, or any other means.
Referring to this object
With vertex colour alone:

With texture alone:

With vertex colour and texture combined:

The final result I seek is a texture alone that looks like the final image.
I have tried jury-rigging it by baking the Vertex Colours to a texture by themselves and then multiplying it with the other texture in an art program - total failure.
Suggestions? Or is it simply not possible?

You can mix the two textures in material or compositor nodes, try the different blend modes. Shouldn’t need another program.