Passing Shapes a StructuredBuffer via DrawMeshInstancedIndirect to render looots of lines

Possibly outside the scope of this forum, but I'd like to be able to render a lot of dynamic independent lines, whose endpoints (or origins + angles + lengths, for example) are stored in a StructuredBuffer and moved on the GPU. Ideally, I'd specify the way these lines are rendered by using a 'reference' Line, so they all inherit its properties. 

I tried to do this by writing a modified version of the Line2D shader, passing it a StructuredBuffer to derive its start and endpoints from in a custom vertex shader. However, I think there's a conflict between the SV_InstanceID property I'd normally use to read from the buffer, and something Shapes internally uses.

I'm wondering if I'm going about this the right way, or if there'd be a cleaner way to use Shapes' vert&frag shaders on a bunch of quads I create at runtime using Graphics.DrawMeshInstancedIndirect, inheriting properties from a reference Line object?