You said further up that you tested foil tape around a single coil, and did not get as high of a capacitance as a was apparent with the tapped coil, but isn't a secondary winding of a tapped pickup extremely close to the primary coil? Even foil tape will contain a little more distance between the windings than will the continued winding of the secondary coil. Being able to model this in LTSpice and see the "apparent" high capacitance without actually assigning a high capacitance would be very informative.
Please note that in the pdf article on coupled windings the interwinding capacitance is not even mentioned, even though there is some also in toroidal transformers with separated windings. The reason is that it has absolutely no effect as long as not more than one of the windings are grounded.
IMHO the increased effective capacitance across the active coil is not caused by the interwinding capacitance but by reflected capacitance.
I may assist with the LTSpice model but fear that this would mean hijacking this thread. We seem to have lost the OP a while ago.
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