We've all encountered weird moments of lag that are very unlikely to do with the servers. I don't know if TCP is used as the protocol to connect the games to the servers, but that's usually how it's done. If that is the case, there is a mod, multipath TCP, that can divert traffic around busy parts of the Internet. It might very well improve the game flow significantly.

Copies of the mod exist for all the platforms you support, and almost certainly your servers as well. A faster, smoother game is worth at least a quick look to see if it's useful.