Hey Tom,
I had a look at your file.
The problem is, that your grooves are about 1 Pixel wide, when Baked in a 2K Texture:

Which means they are about half a Pixel in a 1K Texture Bake. With some AA, that gives the result you got.
Solution: use a 2K Texture, or scale your Procedural (using UV Coordinates, instead of Object Coordinates also does the trick).