Thanks, guys. That has given me a lot to think about.
I tried using the #3 approach with Normandy and it really did not work. The background was just too prominent and made the foreground hard to distinguish in some cases. So I tried something mid-way between #2 and #3 which works better. But given the diversity of opinions, Chad's suggestion of providing alternatives may be the best approach. It had never occurred to me but no doubt this is because it means more work. Thanks Chad.
In terms of the readability of data, here is a sample using #1, #2 and the new #3. As you can see, #1 is the best, as you would expect. All seem readable but since I will use many different background images in different games, not all will necessarily produce the same results.
Also the clarity of the text in the above example is because I am using the Windows option to override high DPI scaling behaviour. If I remove this setting the text is less clear as in the examples below. In the first column are samples of #3, including a Rumanian unit at the bottom. The second column shows the same units but with the stock backgrounds. This provides a comparison which suggests my #3 versions are not as readable as the stock versions. But I believe my version #1 would be at least as good as the stock versions and possibly better in some cases.
So it is back to the drawing board. I will see what I can come up with.