Some additional info, which backs up most of my earlier findings (and confirms the Quantec frozen reverb) and is worth posting here.
From an interview with Kate Bush, International Musician, Oct 1985:
RUNNING UP THAT TRACK
(The making of the single)
Running Up That Hill all started off on the Fairlight. I just found this sound that I thought was a brilliant sound for the riff, and I knew I wanted a military drone-like atmosphere that would surround it all. I asked Del to set a Linn pattern—I sung him the part—and he got that together, and we set that to play the pattern round and round and I worked out the vocal that would go over the top. The lyrics for the first verse came straight away. I stuck it down like that with the voice, Fairlight and drum machine on my home eight track.
"Then we started work on the drone. We froze a three or four note chord from the Fairlight into the Quantec. Already it was quite there, so the next stage we transferred the eight track to the 24 track and we kept the original Fairlight; I added new Fairlight playing the same part because the problem was the sample was actually very noisy. It was called a harp, but it wasn't one. Eventually, although the Linn pattern was used for a long time, we actually ended up putting it down again over more tracks.
"Then we got Stuart (Elliott, drummer) in, and because the Linn pattern was so full in itself it was just a matter of him sticking a snare down. The original Linn pattern had a snare down, but it's not very good and needed bolstering up. We needed something at the end so he put down some very dramatic fills that were a combination of three different sounds, including something on the Fairlight.
"Then I put the backing vocals down, which apart from the weird ones at the end were done at demo stage, but we re-did them. Paddy (Bush, brother) came in and put down some balalaika on the choruses to give them sort of push, Del put some bass down that was very much in there with the toms to emphasise that rhythmic feel, then it just needed something at the end. I put some freak-out voices over it all and all it needed was a guitar to finally build it."
She also mentions in a few other places in the piece about adding real drums over the top of the Linn, including ethnic drums and other things.