No, the jar you posted is fine, it will work. When they say neck, they mean a neck that is narrower than the body, which that isn't. Its wide enough.
My jars are something like 450ml, so larger than recommended, and also straight like that - no taper out. They work just fine.
I'm still working on my recipe for the contents of the jar, so I'd probably stick with the PF tek if I were you. I'm trying to find something different because I don't like vermiculite, as its not sustainable.
Paper kitchen towel works well as a barrier for the top of the far, to keep microorganisms out. That and foil of course.