The measurements from the non-gapped device showed a dramatic increase in L with increasing signal. It makes sense to me that this would not be a good thing.

I'm sure the 'White Paper' writers and supporters will have something silly to say about gapping inductors with no DC in their use profile...:) I got the C-core ones made so I can experiment and those measurements I'll share, including how they sound. These I got wound so as to maximize leakage L, and minimize end-to-end capacitance. I will include some comarisons to other available grid chokes for Cw. To hell with the idea of not publishing that info...:)
cheers,
Douglas