How do I fix UV Mapping after Boolean Union

I am trying to figure out the steps to use, and a workflow for combining models using Boolean Union.
Some of the models already are created and have textures on them. I want to use Boolean Union to get a single mesh that is manifold for 3D printing, so a Join will not give me an acceptable mesh. Also the models already have textures, and I want the resultant to keep the textures from the original models. These will be needed in exports.
I started testing with a simple cube and sphere model. Each with a simple image texture. I unwrapped each and setup each with UV maps and they looked good. Added new file and Appended the cube and sphere objects from the simple blend files. Then I used modifier on the cube to do Boolean Union of the sphere. I examined the mesh and it looks great. Blender did a nice job of creating new vertices and stitching things together. I know there are some improvements I can do on the mesh, but for this test it is fine.
The problem is with the textures. The 3D view actually looks like what I want, the cube section has the texture from the original cube, and the sphere section has the texture from the original sphere. You can see this on the left in the image above . But when I render, the texture image from the box covers the entire model. Also there are only the material and the texture from the cube listed in the properties. Those for the sphere did not make it in as a result of the Boolean Union. But somehow the 3D view gets the texture from the sphere model. Note - I did delete the original sphere after doing the Boolean Union.
The UV map is shown in the image, and it has overlapping UV maps from the sphere and the box. I would like to be able to use the islands in this UV map from the sphere with the image texture from the sphere, and the islands for the cube section with the image for the cube. Finally I want to have one UV map with non-overlapping islands and bake everything into one texture.
Does anyone know how I would go about accomplishing my goals here in Blender? I have looked through the forums and tutorials but have gotten stuck at this point. Maybe there are some setting or options that folks know about that will help me here.
Also if there are any tutorials that anyone knows of that cover what I am trying to do, a link to them would be greatly appreciated.