I'm using a NewHaven 40x4 display ...
Specifically, which NewHaven display are you using? At least some of their displays, while mostly HD44780 compatible, have some slight differences in one or two commands. The commands I know about that are different are concerned with clearing the display so I don't think they will affect your problem.
... and LiquidCrystal440.h library.
I guess you know that this library is for the older versions of the Arduino IDE.
Don