I understand where you are coming from and I wasn’t intending to throw a monkey wrench into your idea.
It just occurred to me that this could be a kind of sneaky way to win, as long as they had the other requirements.
Then I remembered that these requirements have to be met at the end of a full round and it occurred just as quickly that it would be a stupid move on the Axis’s part because then the Allies could pick up even more IPCs and maybe be in a better position to win on your terms.
If I were you, I think your first idea of simply making the strict neutrals off limits for this type of game would be the best idea. Trying to add the strict neutrals would mess up the totals too much, particularly if you got to playing and suddenly no one decides to attack the strict neutrals after all. Also, like you mentioned, a lot of them would really be out of the Axis’s range anyway. Practically, the only strict neutrals that are worth IPCs and are within the Axis sphere of influence are Sweden, Spain, Portugal and Turkey. Maybe Saudi Arabia if they go strong after the Middle East. So including the strict neutrals would probably be greater impact to the Allies, maybe too much so.
Another idea would be to make all the strict neutrals pro- one side or the other. This way perhaps the Axis might have a little better chance and even if there are some that are out of reach for the Axis, like Argentina being Pro-Axis for example, the Allies would have to fight to take it.
Making strict neutrals off limits is probably the best and easiest idea.