Ken, KC2JDY wrote:
"If I put another 23 ft wire to the radio ground and run it off as
closely as possible to 180 degrees away from the first wire, will this
necessarily (likely?) improve reception?"

Short answer: Not likely.

Regardless of transmitter antenna polarization, received signal
reflected by the ionosphere has random polarization. About equal amounts
of vertical and horizontal polarization are available for reception.
It`s the way the ionosphere works.

It`s advantageous to use horizontal polarization in a receiving antenna
for ionospheric signals. It`s because horizontally polarized antennas
reject vertically polarized signals and it`s said that most noise is
vertically polarized. That`s largely because there is no ground wave
propagation of horizontally polarized signals. The ground reflection of
a tangential wave has the opposite polarity to the incident wave. The
sum of the direct wave and the reflected wave along the surface of the
earth is very nearly zero for horizontal polarization.

A vertically polarized incident wave and its reflection are "head to
tail" like flashlight batteries and this is obviously constructive
rather than destructive. Even so, the earth is lossy at high
frequencies.

Received vertically polarized signals come from afar via the ionosphere
or via line of sight. Some ground wave propagation exists but it`s very
poor. Received horizontally polarized signals come from afar or from
very near because the earth treats them so badly. No ground wave exists
for them. Excluding vertically polarized signal reception excludes
nearly all out of sight signals except those reflected by the ionosphere
at shortwave frequencies.

Noise is worse the closer it occurs to the receiver. Noise from a
distance is weaker, in general.

Horizontal polarization is a noise suppressor.
A balanced antenna system is a noise suppressor for much the same reason
that a balanced transmission line is a noise suppressor. To the extent
that noise induces a common-mode signal on both wires, it balances out
in the receiver provided the receiver is not unbalanced.

The problem with adding a balance wire to the ground side of the
receiver input is that it is likely that the receiver input is already
unbalanced. It likely already has a ground return for the antenna
circuit, either directly or through a capacitor, to complete the signal
path for an unbalanced antenna input.

A balanced antenna system could be used with the receiver to improve the
signal to noise ratio by inserting a balun at the receiver between the
balanced horizontally polarized antenna system and the unbalanced input
on the receiver.

Best regards, Richard Harrison, KB5WZI