Well, I didn't say it was definitely Hamachi. But, as you say, that's the major thing that you changed aside from switching who you were playing with. Glad I could help insofar as I could, at any rate, and I'm glad it's working for you now!
The Ctrl-+ network command is really kind of outdated, it was primarily useful back when we used TCP networking instead of UDP. That runs more game cycles per game turn, and thus fewer turns per second. The purpose of that was to give TCP packets more time to resolve themselves in high-latency situations, but so far as I know no one is still using the network command speed adjustment any more, and there's not really a reason to. UDP transmission being what it is, most likely it is unlikely to change much unless there is a really tremendous amount of packet loss or really high roundtrip times for some reason. That isn't supposed to affect the network timing, but I haven't messed with that command much since switching over to UDP a few months ago (August, I think it was). Even in cases of extreme latency, I think that +1 or +2 would be the sweet spot if you were to get use out of it, but I think it's mostly no longer going to be much benefit. Were you having a lot of lag?