I need a Geometry Node setup that would let me select just each of the long edges (basically the blue lines) and then convert each long edge into a curve, keeping the same points along the way and any curvature that the mesh may have.
It could be just some general plane mesh of some sort of length, with x number of subdivisions along the long edge but only 0 or 1 through the long length.
So this could be ‘hand’ made or as part of an earlier nodes setup.
I’ll give your Index option a try, which in theory should work, so will see.
Using the Shortes Edge Paths node is a great advice!
Combining it with the Edge Paths to Curves node and and iterating over every point in the mesh, you should get the Edge Paths going from any point to every other point in your mesh. The “only” thing you then have to do is to filter out all the curves you don’t need (e.g. curves with an abrupt direction change or smaller ones).
Of course it’s easier to just select the edge loop you want instead of letting an algorithm figure it out.
But keep in mind that my solution doesn’t necessarly returns edge loops only! It’s just the shorteste path from one vertex to another. If that is a requirement you could adjust the setup from the link i posted above and loop over all edges to find the largest edge loops in the mesh.