Can you still capture the rest of the territories after you conquer all the strongholds?
Or do you need to capture all territories before you capture the last stronghold to beat the map?
You can conquer territories after all the strongholds.map wont end until all territories are conquered.
I would recommend getting a bunch of territories around your start spot on usa map, it will give more fans that will speed up going for strongholds and provide a buffer and slow the other teams down a little.
There is a great tutorial on youtube about how to beat it. First capture the area around starting stronghold, then fortify up to four because AI will not attack it until later. Capture all the territories before capturing strongholds.