Just doing some googling on coil materials/winding methods (to see if I need to go to the expense of sourcing decent litz wire or sticking with my copper foil experiments) I found this puppy...

http://powerelectronics.com/passive_components_packaging_interconnects/resistors/807PET-high-frequency-inductors.pdf

Does this suggest that as well as having a gap in each ferrite bar in the centre point of the cylinder (to reduce eddy current creation?), we should also be looking at increasing the diameter of the coil winding as it goes across the gap? - To reduce ac losses in the winding?