John Popelish wrote:
. . .
I think I agree with just about every conclusion you are making about
treating coils as slow wave transmission lines. . .

A coil itself isn't a slow wave transmission line. In conjunction with
shunt C, it can be analyzed as a transmission line, but only in
conjunction with shunt C. Remove the shunt C and it ceases looking like
a transmission line. The earlier example of the modification to Cecil's
EZNEC model illustrated this -- when the ground (the other side of the
shunt capacitor) was removed, the current drop across the coil disappeared.

As far as considering a coil itself as a "slow wave structure", Ramo and
Whinnery treat this subject. It's in the chapter on waveguides, and they
explain how a helix can operate as a slow wave waveguide structure. To
operate in this fashion requires that TM and TE modes be supported
inside the structure which in turn requires a coil diameter which is a
large part of a wavelength. Axial mode helix antennas, for example,
operate in this mode. Coils of the dimensions of loading coils in mobile
antennas are orders of magnitude too small to support the TM and TE
modes required for slow wave propagation.

Roy Lewallen, W7EL