First of all, this 15-475-011 Special Tool Kit would be incredible given its completeness - with the original drawing tucked into a pocket, no less, regardless of the provenance. The fact that it was your Dad's makes it beyond special, and priceless. My Dad was also a WWII vet, Navy, and we found so many things he never talked about, including his ship's home-made newsletters, for which he provided all the artwork. All I can say is, it figures that it was tucked away in a toolbox and you don't know much about it. When I hear the guys in the 'Band of Brothers' type movies and documentaries, all I can think is, it must have taken a lot of cajoling to get them involved, because my dad and my uncles had no interest in talking about the war.
Re: the drawing. It was used to track changes to the kit. I have analyzed many from the Willys-Overland factory for the evolution of the jeep toolkit and a chapter in a book I co-authored on that subject. Every time there was a change to the kit, the drawing was updated, and the change annotated by date. You have posted a zoom on the change block and the whole middle. Would you please post a zoom on the lower right? That is where the most helpful identifying information will be. It will include the name and part number (judging by the pouch, and the watermark on the drawing, looks like 15-475-011) of the kit as well as dates and responsible agencies and other helpful information.
Is that how you're connecting this toolkit to the "Peashooter" (P-39)? Does it say P-39 on the drawing? Did you search on the part number? Or are you using a priori information with respect to your Dad's wartime career? Also, what are you using to infer that it was a "prototype" kit? The P-39 was tested as early as 1937 and involved in the war very early. On top of that, the drawing is from late 1943.
The kit looks to me like it was specifically used for maintaining .50 cal machine guns. I see multiple references to ".50 cal" on tools and the pouch. (Very interesting how they re-purposed a Williams water pump wrench for a .50 cal adjusting nut!) My understanding is that the P-39 had two .50 cal MG's early war (slotted in each wing near the fuselage), and then four (4) late war. Do you see a ".37mm" anywhere on the pouch or the tools? The P-39 was famous for its nose cannon. Perhaps there was a separate kit for that gun.
Love it. Trying to help.
Please post that lower right corner of the drawing.
EDIT: The drawing is the key.