The Greyline is not the typical Vertical....it is balanced OCF Vertical Dipole.
Quote from Greylime
"The flagpole must not be fed unbalanced. It is an electrical-half-wavelength vertical dipole. Both ends are insulated from the ground and the off-center (OCF) feed point must be provided with a balanced feed."
Well, yes, that is the manufacturer's claim.
But
that might not be the actual way it operates.
If it is significantly less than 1/2 wavelength long, it is unlikely
that it is actually working as an OCFD in the conventional sense.
If Owen's analysis is correct (I don't have an antenna handy
to test), then, the better the balun, the worse performance is
likely to be. With a mediocre balun, the ferrite will act as a
load resistor in series between the bottom of the antenna
feedpoint and ground. That stabilizes the impedance at a value
suitable for many tuners, but reduces the efficiency. The better
the balun, the higher the series impedance, the higher the losses,
and the more difficult the impedance is to match.
A quick check would be to remove the balun, connect the tuner
directly to the antenna, add some ground radials or a ground
rod, and see if the antenna works better in that configuration.
Of course, this all also depends on what tuner you are using,
as all tuners have limitations on what impedances they can match.