In Pufferfish I have Unsplit Surface components for this. Use Extrude Unsplit Surface with the profile.
Before baking run the Rhino command CreaseSplitting and change “Split Along Creases” to No, then bake from grasshopper and you will get one surface with creases.
If you want to do it in Rhino to existing extrusions, explode the polysurfaces and use the command _MergeSrf command with roundness set to 0. You can only do this by pairs tho so you will have to do it for each crease. You will get this result.
To your question about splitting them, I would split the profiles at the tangent discontinuities, then extrude.