Andy, I am confused, how do you attach a long wire to a balon? since
a balon has a balanced output for two wires and a long wire is just
that, a long wire.
Your tuner should have a long wire output, which might and usually
plugging the wire in there, or using the center of a coax output,
yields the same results.  In your case, that is not the
case.  Easiest thing I can think of, is to attach the wire to a
banana plug, and change tuner connections for the desired band.