Hello, author here with a weird random name, lol. I apologise that I'm forgetting to check when I'm tagged in a post.
I don't personally like parallax on anything other than flat-ish vertical geometry and floors/terrain in this game. Parallax does have a number of implementations though, and the more expensive ones, like cone stepping, are better than the older parallax methods authors' have implemented into Skyrim - offset and occlusion mapping. Still, all of these methods can't really do much with texture edges/seams on a model because parallax is still only faking 3D. Reducing the effect strength across the board is going to be the only fix I can think of, other than not using it on certain meshes.
Anyway, why am I offering it then? Well, because I will get spammed with requests. Parallax = hotness. Really though, it's not up to me to push my tastes on others. I could mention my tastes and suggest the base option, but then you will get whispers that the parallax version is "broken" and to use something else. This would be unfair when there are many external variables at play - texture packs, ENB settings, user error ect.
You can also visually check out the many implementations of parallax on this old program here: http://www.brunoevangelista.com/wp-content/uploads/2010/03/detailed_surfaces.zip