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But in this case, it is a virtual machine running Arch Linux (the Synergy client machine is running Windows 7), so changing virtual terminals would be fine. So I needed to find a way to change virtual terminals besides using the Ctrl-Alt-Fn keystrokes.
Enter the 'chvt' command. It needs to be run as the superuser, so issuing this command swaps the virtual terminal to terminal 2:
$ sudo chvt 2
So now I can swap virtual terminals in virtual machines even if I can't get the fancy keystrokes to go through to them.
chvt(1): change foreground virtual terminal - Linux man page