Unfortunately, this is most likely an
ISP issue, though it could be caused by a low-strength wireless signal or bad router or something else. I would suggest doing a
traceroute in order to determine when the latency strikes -- is it between your computer and your router, between your router and your ISP, or between your ISP and the destination on the Internet. If it's the latter, you can call your ISP and see if there is anything they can do, but as the first linked article notes, they are not obliged to. Sometimes calling and complaining will get them to fix issues on their end, though -- one of my alpha testers had to do that with Comcast, and they fixed his issue for him.
Given that this is something apparently pervasive with your network connection, there is not anything that AI War or any other game can really do to work around it; performance in a game depends on how much ping latency can really be absorbed. Some FPS games send little enough data that they can absorb as much as 1000ms of latency without being unplayable, but due to the network data volume of AI War, any ping over 200 is going to start hurting unless you use the network+ tool that you already were. That basically allows for larger pings, but causes higher command lag in return (given that it is waiting so much longer between transmissions to account for the bad ping). Generally that's going to be a pretty bad tradeoff above network +5 or so, and preferably that network+ option would not be used at all.
Hopefully using a traceroute you can diagnose the source of your bad ping, and then either fix the wireless connection, fix/replace the router or network card, or badger your ISP about whatever is going on with their service. Wish I had better news, but this is well below the level of the game if you are seeing those pings outside of the game, and is something you'll have to diagnose for your specific case. Good luck!