Is it “Vinicultores Illustrissimi Hungari” grammatically correct?

I found the following inscription on the cover of a "Codex vinorum" (a box for wines): "Vinicultores Illustrissimi Hungari" (as I would translate: the most excellent Hungarian viticulturists). I would like to give this present to a Latinist and I have the possibility to have this inscription changed. Is it grammatically correct with the two attributives put after the noun? Is it generally used in Latin language "Hungari" as an attributive or "Hungarici" should be used? Isn't it possible that instead of this inscription the following would be better: "Illustrissimi vinicultores Hungariae"? Thanks in advance for your help!