Best projection for preserving parallel lines?

[cantab]

Hmmm...and now I realise that the concept of a parallel line, in the geometric sense, isn't even clearly applicable to spherical geometry.

So rather, I think I need to construct a great circle that intersects the ridge at right-angles, then construct further (segments of) great circles at right-angles to that. (This is hypothetical; I won't actually need to go through those steps, I'll just do parallel lines on the map.)

That tells me I need a conformal projection and straight lines on the map need to be as nearly great circles as possible. Distance preservation is less of an issue since I can use the software to find the true geodesic distances.

This points me, I think, to an azimuthal stereographic projection. (Or rather a set of them, each centred on a different area of interest).

EDIT: And while I was writing that post up I see Hai-Etlik has beaten me to it. Maybe his suggestion would work better.

EDIT2: And now I'm reminded of something I overlook before. Over a long distance, the "parallel" line isn't the same distance everywhere from the ridge - for the ridge itself spreads at different rates along its length. However, since I have lots of short segments I can probably treat each piece as an equidistant line.