I have a very small yard and a 70ft tower with a beam on top. I want to put
up transmitting antennas for 80m and 160m. For the space I have, some form
of vertical seems the best. I do not want to shunt feed the tower as a
vertical because the feed lines run a long way to the tower from the house
along a messenger cable that is 10ft above the ground (no buried coax). The
feed lines would become part of the radiating system and would put a lot of
RF into my shack.

Shunt feeding the tower is probably the simplest option.
Why not coil the feedlines into chokes when they leave the tower, or
put stacks of ferrite beads on them to keep RF off them?

Torsten
N4OGW