Wouldn't it be better using wireguard at this point. I thought hamachi was long past it's prime.

As for alternatives, I've heard lots of good things about Tailscale (or headscale if you want to self host).

If them connecting to you is an option, WireGuard is also stupidly easy to set up and very reliable. If you need to also forward layer 2 traffic (old LAN games and weird local protocols), you can use OpenVPN for that. A bit hard to set up but also quite capable.

After having that same issue with haguichi, I switched to using hamachi in the terminal only and haven't had it happen since.

I haven't tried to use hamachi in years so I'm not sure about a solution to your problem. However, I can strongly recommend Zerotier as a potential alternative

Unfortunately that trace isn't very useful due to the lack of debug symbols. One would have to decompile and analyze the binary to really gather some information as to how that happened, and it's probably against their TOS.

hamachi will occasionally disconnect *and then ask for my password to restart the service. *

The GUI is probably trying to restart the daemon for you which causes this, because that's not standard behaviour. You can probably fix that but just allowing your user to do that passwordless, although it's dumb:

# /etc/polkit-1/rules.d/50-hamachi.rules
polkit.addRule(function (action, subject) {
    if (
        subject.user === "YOURUSERNAMEHERE"
        && action.id === "org.freedesktop.systemd1.manage-units"
        && action.lookup("unit") === "logmein-hamachi.service"
    ) {
        return polkit.Result.YES;
    }
})

You'll want to change your username in there and also adjust the service name if it's different.