Thanks for posting a picture of the northern polar version of the map and providing the additional background information. I think the northern version has good potential to be developed into something that could work quite well. I’ll get to the specifics in a moment, but first I’ll run through the decision hierarchy which I think is involved here. The highest-level choice is of course the decision to go with a circular map rather than the conventional rectangular shape (or possibly some of the other broad types of map projections which exist, such as the ones which are oval or losenge-shaped). A circular A&A map isn’t personally something I’d use for gaming, but that’s just a personal preference – and as a Global 1940 map customizer myself, I totally see the point of wanting to do something imaginative to improve the OOB game board. With a circular projection having been chosen in a general sense, the next decision becomes which specific circular projection to use, since there are several types, azimuthal equidistant being just one of them. Choosing azimuthal equidistant then leads to the decision of which particular view to use: north polar, south polar, equatorial or oblique. The equatorial or oblique views strike me as the least suitable options for A&A gaming purposes, by a wide margin, which leave a choice between the two polar views – which is actually where we are in this discussion.
As your new picture shows, the northern polar view gives the following cost/benefit trade-off. The cost that it more or less throws Antarctica under the bus; this is actually a pretty trivial cost because Antarctica isn’t a usable territory in A&A, so you’re not losing anything (other than perhaps the potential for some house-ruled secret Nazi bases) by turning it into some white squiggles around the perimeter of the map. The benefit is that it gives (compared with the southern polar view) the most square footage and the least shape distortion to the northern hemisphere, where most of the world’s land mass is located and where most of the land-based action of WWII was fought. As a basic choice, this strikes me as being optimal.
What would remain at this point would be the issue of adjusting the details of the northern polar view to make its land and sea subdivisions as usable as possible as a physical A&A game map on which sculpts and territory markers and so forth can be deployed in adequate numbers. As is the case with the rectangular OOB map, this will – regretably but unavoidably – involve making selective size and shape distortions. China on the OOB Global 1940 map is a good example of what I’m referring to: compared with how China really looks on a real map, the A&A version is a fair approximation in terms of shape, but in terms of size it’s extremely compressed in the east-to-west direction relative to its north-to-south size. For your northern polar map, I think the first element you should target for adjustment is the problem you’ve mentioned yourself: the fact that most of the map is water. In real-world terms, the Pacific Ocean carries much of the blame: I think it occupies about one-third of the world’s surface. The Global 1940 map massively shrinks the Pacific Ocean, and even cuts out sections of it entirely (notably the huge area between Samoa and South America). So what you may want to do is measure the surface area allocated to each ocean on the Global 1940 map relative to the total land area, then replicate the same size ratios on your northen polar projection. That by itself may give you more than enough room to expand the land areas to a conveniently usable size.
