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Realigning Panner Direction?

I’m making a spline-based river system, but I’m having trouble with the river surface material, specifically with panning the texture. It works fine lining up the straight-direction panning, but when I want to curve the river direction along the x/y axis, I’m having difficulty figuring out how to adjust the pan direction to match the direction that the river is turning.

Examples:

Correct

Incorrect

The best way is UV the river so that it’s straight in the UV map, it’ll look like it’s flowing along the river.

It’s straight in the UV, but the spline is duplicating the mesh and then skewing it to make the curve, which doesn’t angle the uvs in the new direction.