How to stop flickering when using Line Renderer and any camera follow script?

I've hit a pretty hard wall in my game development... for aesthetic purposes, I'm trying to give the game a vector-based look, which includes using the line-renderer to make thin lines. From overhead view, I have a triangular spaceship and a 0.01-width line (to be used for making walls).

When viewing things through the Main Camera it works, but as soon as I use any 'camera follow' script to follow the ship, it causes the line to start flickering, which gets amplified with post-processing fx.

I've tried many things to stop the flicker:

• orthographic vs perspective camera

• varying the line size (anything below ~0.5-width has noticeable flicker)

• rendering the line through different methods (e.g. bitmap, shader, Vectrosity, etc..)

• several different camera-follow scripts, from default Unity asset scripts to online posted code

• moving all combinations of ship and follow code with FixedUpdate, LateUpdate, Update

• changing clipping planes, above Near: 0.3 below Far: 1000

• different rendering paths, deferred, forward, legacies

• using 2 cameras with depth masks, culling and layers, main camera renders ship, the other renders line with either camera having ship-follow script attached

• changing anti-aliasing 2x - 8x

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I am certain the problem always begins when using a ship-follow script, but using one seems necessary. A slight observation I noticed is if the ship moves straight along the same axis as the wall, there's no flicker i.e. with a horizontal wall, flying straight left or right causes no flicker, same with vertical/up-down, any movement along the other axis causes the flickering.

I've searched for answers online, but oddly enough I don't see a post about this exact issue. Is there something more I can try?