What do you need Hamachi for? You can configure your own router to forward to the server, or set up a VPN to connect them.
It’s likely that the network connection or the hardware (router etc) simply can not handle the amount of traffic quickly, but it could also be Perforce itself or the size of the repository. For that you’d need to perform some tests to be sure.
I’m still a huge fan of Git. I tried Perforce and Plastic and I was seriously disappointed by the lack of control I had and complexity to port my existing git repo (which eventually just didn’t work out). So I sticked with git. If you wonder about how to use git in a team and with binary files there seem to be some developments to improve that. there’s a Git plugin on the marketplace to work with a team (and lock binary UAssets), but I have not tried it. Also the new version of Git lfs might have proper ssh support now, I read about it on github a while back.