NO9E has the best idea. Feed the 80 meter dipole with ladder line...
This, of course, won't change the radiation pattern.
But let's consider the current distribution on a vertical antenna for a moment. The current
is maximum at the base, or 1/4 wave down from the top for antennas longer than 1/4
wavelength. As you increase the length to 3/8 wavelengths, for example, the feedpoint
impedance increases, and the portion of the radiation with the highest current (which is
responsible for most of your radiation) moves higher up the antenna. This helps to reduce
your ground losses. Above 5/8 wavelength the pattern breaks up in to higher lobes, making
it less useful for DX, but verticals longer than 1/4 wavelength can be good performers.
Now not everyone is able to put up a half wave vertical for 80m (~125' tall). But you can
use a top loading wire strung between two supports to replace the upper part, since that
doesn't contribute much to the radiation. This becomes a "T" antenna.
Taken to the extreme this becomes a half wave horizontal wire with a quarter wave vertical
wire connected in the center, dropping down to a feedpoint at ground level. Maximum
current is at the wire junction, elevating the radiation above some of the ground clutter
that can cause issues with shorter antennas. Sometimes this is called an "inverted ground
plane" because it is, essentially, a quarter wave vertical with two ground plane radials
turned upside down and fed at the far end of the vertical section.
Now, compare such an antenna to the dipole you have in place now: both are 1/2 wave
across the top with a wire running down to ground level. The only difference between
the two is that your dipole uses coax or other feedline, while the inverted ground plane
has a single wire. All we have to do to switch between the two is to connect the two
ends of the feedline together (whether using coax or open wire line) and feed them
against ground. A switch or jumper plug can do this quite easily, giving you the ability
to switch between vertical and horizontal polarization with the same antenna you have
in place right now. (Though it will probably help to add some radials.)
Note that the feedpoint impedance will be high in vertical mode, so you'll need a tuner
or some other way of matching the impedance. One solution I've seen is to feed the
antenna with open wire line, in which case the feedpoint impedance will be high for
both modes, then use a parallel-tuned network for matching. Another way is to
use a quarter wavelength of open wire line from the switch to the shack: that gives
a total of 1/2 wavelength of line on 80m in dipole mode, providing a good match to
50 ohms. When the antenna is switched to vertical mode the same feedline works
as a zepp feed, and the impedance should be within the range of a typical tuner.
That's why I made my earlier comment - you can use your existing dipole with vertical
polarization and not have to string up a second antenna to try it out.