You're correct that the feedline and/or tower are part of the antenna.
What you have is a dipole (not necessarily symmetrical), with one side of
the dipole being the half-sloper "antenna" and the other side being the
tower and feedline. The feedline has two transmission line conductors,
which are the center conductor and the inside of the shield. Whatever
current flows out of one must flow into the other. The current going to
the half sloper equals the current flowing down the tower and outside of
the feedline shield. If you effectively choke the tower and feedline
currents, you'll also choke the current to the half sloper.

While you can effectively choke the current on the outside of the feedline
(it would probably take two chokes, one at the top and one at the bottom),
it won't help your noise situation. Whatever nearby vertically polarized
noise might have been picked up by the outside of the coax will still be
picked up by the tower. If the problem is vertically polarized local
noise, the only solution is probably to go with a fully horizontal antenna
with a well-decoupled feedline.

Roy Lewallen, W7EL

Thank you for the confirmation. I'll skip the choke for the half-sloper.

I am aware that many hams take a poor view of these antennas. Perhaps I
am a bit lucky because mine seems to meet my minimum requirements ---
especially for transmitting ---
probably because I do not use 80 or 160 very often. (I still need about 25
countries on 80 for 5BDXCC and this is my driver.) I would love to have
a quieter receiving antenna for 80. There is a very interesting scheme in
the
QST I received today; in effect a rotary beam for 80, with variable angle
of reception.

Bill - W2WO