I have been following this thread and just picked this point
to jump in.

I also have pondered how a core and coil structure might be
made that would allow the flux in one section to be
saturated without coupling the signal from the unsaturated
part into the saturating coil.

I think your toroid in pot core gap structure would work
best with the entire surface of the toroid wound with fine
wire (two layers, around and back to the starting point, to
avoid a 1 turn "secondary" of the pot core "primary").

This structure does provide a small gap (at least two toroid
winding wire diameters) in the pot core flux path, but a
variable gap, none the less.

The problem with your notched toroid structure, is that
there is a flux path across the notches, through the pot
core material that detours flux that would otherwise go
around the toroid, so you end up only saturating the toroid
under the windings, not all the way around.

You could also just wind the assembled pot core toroidally,
so that the toroid winding is used to saturate the entire
hollow center leg of the pot core. This would work best
with a pot core that includes a couple (or more) slots along
the outside circumference to bring the core windings out
through, so that only the center, hollow post is saturated.