I went and looked up some more about the Axeman and all but 2 of his alleged victims were Italian. Fi na Ne most likely is a varient of Fine meaning "Done" or "Finished". I'm settling into my theory now. There was some thoery that the Axeman was named Joseph himself but that couldn't be proven conclusively (Joseph Mumfre) but it makes sense since he singled out The Feast of St. Joseph in his famous threat. Feast of your the Saint of your name was and remains a big deal to Italians (and Irish Catholics to a degree).

I may be alone in supporting this derivation, but I'm liking it more and more.