How about this untried idea.

A latching relay.. switched by a battery in the loft.
When you PTT up coax 1 a transistor is biassed to pull
the relay across to that coax and disconnecting the other
coax. I larg-ish electrolytic capacitor and resistor in
parallel as the relay sink, so the relay current drops off
to almost nil once it's changed. This would reduce overall
current drawn from the battery.

I wonder if something like that would work well?

Rv!