I'm wondering whether some sort of corkscrew-shaped mirror assembly along the middle of the tube would help with this, reflecting more of the light past the arctube from the inside of the spiral?

It won't help, the geometry just won't allow to utilize all the light and still fit into the gaps. At best you end up with the same overall efficacy. Well, unless the spiral isn't very wide open t start with, but then it would have lost the benefit from being the spiral in the first place.