The 337 was used in all the Lincolns but only from 1949 thru 1951. Same for the F7 and F8 trucks. FoMoCo always had modest production numbers for high end cars and very big trucks so the numbers probably aren't all that impressive for the 337 CID engines. Definitely not as impressive as passenger cars and lighter duty truck production numbers.
The war years have always been kind of a mystery except for those that might have done the research. Most of the USA produced military vehicles I've seen from that era are either small jeeps (many made by Ford), larger Dodge type ambulances & wepons carriers, or the larger 4 or 6 wheel drive trucks that were made by a number of motor companies. Many of the big trucks & half tracks had flathead 6 engines from Hercules, GMC, Leroi, White, and many others. I'm still currious what all Ford might have made in that time frame that had flathead V8 engines. Canada and even the Axis powers produced a lot of V8 powered trucks & gun carriers but the USA I don't know.