USS New Hampshire (BB-55) Reboot II
The basic assumption is that the terms of the Washington Naval Treaty failed to be agreed upon. As such the South Dakota-class battleships were never cancelled and in fact was followed by USS New Hampshire-class a behemoth dreadnought heavier and nearly as long as the Iowa-class, sporting a main armament of 8 eighteen inch/50 caliber guns, 24 six inch/53 caliber secondary battery and 8 five inch/25 caliber dual purpose battery.
Well, I've replaced the bridge superstrucrure with one which combines features of both the New Mexico modernization and the South Dakota. Furthermore, the USS Pennsylvania (BB-38) entered the Philadelphia Naval Yard for modernization during the period of May 2, 1929 to May 25, 1931 where her cage masts were replaced with tripod masts. This being the case, it seems likely that any new battleships constructed during this milieu would also have been completed with tripod masts similar to those found on the Pennsylvania and her sister ship Arizona. I have redrawn USS New Hampshire along that thought using tripod masts.