Hey MSR
For what you are looking at, any coax cable is going to be a very (!) bad idea. I don't think I have to re-hash all the reasons.
I have a very similar situation where I am--- there is a granite escapment that shields my place from a valley I wish to launch a VHF signal into. It towers over my house several hundred feet and effects a perfect shield in that direction.
Until lately I had run a Goubau feed line up to the top and fed it to a beam antenna.
. I have been meaning to write up this unusual topic for some time. Then a weather event this week brought it back in sharp focus with a snow storm and high winds. All night long this storm raged, and in the morning I was greeted by its twisted mass buried in a snow bank. Caught your...
forums.radioreference.com
The ice we have at +9800 feet took it down this winter
_______________________________________________________________________
I would not suggest one of these in your case--- the design at 27 MHz is going to be too mechanically awkward.
But will suggest this:
Ok, take a seat---

You sound like a bloke whose up for a challenge-- at least enuff of a challenge to go string'ing feedlines up a mountain side. What you need to
consider is the use of an open wire feedline-- suspend it from poles clearing the ground all the way up to the summit (it going to look like an old fashioned telephone line) -------I'd use, in your case, spaced line 6 inch line.... buy it or make it yourself. It will be a project (!), but you leave few other (reasonable) alternatives.
Years ago I knew a rancher in Wyoming with just a similar case as yours. A tall steep hill shadowed him from a (then) analog TV station. He did exactly this---ran a open wire line from his house, over 1500 feet, to a TV antenna. A kind'a snowy picture, but it worked well for what he wanted.
Good Luck Cowboy !
Lauri
.