I say "I have need of..." often. I am a native American English speaker...from California. My husband teaches writing and composition at the university level. My phrase is neither archaic nor incorrect.
I don't see what your state of origin has to do with this. I am a third generation native southern Californian. I never said the phrase was incorrect, but I still contend that the phrase, "I have need of..." is not common English.
The problem I see of translating into "modern American" is you do not learn the italian construction for when you say it in italian
So I have need of is better for me
(I've need of" is a phrase commonly used in English especially northern English)