I don't know why Verschuur feels obligated to invoke "magnetic reconnection" here, or even Marklund convection for that matter, which separates ions by ionization energy, but which doesn't produce oppositely charged regions.

But what mechanism would simultaneously act to clump the neutrals and the electrons and have them physically separated yet closely associated in space?

This is easily explained just with basic EM principles. When like charges are moving in the same direction, their combined magnetic fields push them together (i.e., the magnetic pinch effect). The corrolary is that the magnetic fields from opposite charges push them apart (i.e., the so-called "magnetic push" effect). Yet despite the magnetic pressure, there will still be an electric field between opposite charges that will pull them together. So in space, we can expect mildly separated but closely associated opposite charge streams due to the effects of magnetic and electric fields.