You'll have to forgive this non-Hamilton post but I thought some folks might be interested.
Hamilton wasn't the only manufacturer to make military watches for the US (and other) military. I'm definitely no expert on all-things military watch related but I do find the differences and similarities of various makers interesting.
One of the precursors to the Mil-W-46374B and the GG-W-113 was the Mil-W-3818B made in the 1960s. Military contracts were awarded then just like they are today - through competitive proposals that aligned with military specifications at the time. Specifications defined the materials of construction, accuracy, luminescent requirements, durability, etc. and watch manufacturers would provide proposals to meet the requirements. During WWII there were several awards for various wrist watches and in some cases different manufactures would even make parts for each other.