In this (the last I hope for you ...) report you find the results of
computer simulation of a coil between the top end of the vertical
radiator and the top load wires.

.....

For practical reasons a top load coil has to be of limited size.  I
have modelled coils of 500, 1000 and 2000 microhenry.

In order to present a more useful picture I also included a
loading/tuning coil at the bottom end of the radiator. The coil has
been chosen so that it resonates  the system. The Q of both coils has
been set at 300.

Conclusion: A top coil does not increase efficiency for the
configurations modelled.

This is also a conclusion that would have been made by commercial
nondirectional beacon (NDB) users as there are no loading coils "up in
the air" that I am aware of (but there are resistors inserted in some
cases, to lower Q).

In the amateur case, the quest is for maximised efficiency for a given
QTH and practical antenna mounts, so inserting resistors in the antenna
is not on the agenda.  It is likely that a higher Q coil could be made
for use "on the ground" than for use "up in the air" (mechanical
reasons, and electrical weatherproofing against arcing over).  So using
Dick's conclusion (for equal Q), there is arguably a net conclusion in

The ONLY reason I am aware of where centre loading could actually be
beneficial on LF for amateur type of installations is for the USA
situation where they have a prescriptive regulation that says that
LowFers in the band 165 - 190 kHz can have no more than 50 feet of
antenna, from the transmitter output.  Being bound by such formulated
limits, a pure vertical with centre loading coil is about the best that
can be squeezed out in terms of efficiency, with the transmitter at the
base of the antenna.  Thankfully there are other countries that do not
place physical size limits on amateur antennas, or feeder lengths, so
the benefits of capacitive top loading can be reasonably exploited.  An
e.i.r.p. limit on radiated power is considered to be a far better way of
capping amateur radiated power, to allow for free experimentation and a
lot of fun to be had in warming up the ground :)

Bob ZL2CA