The best way to move all of it would be to select all of the nodes within the automation. I don't know if there is a shortcut for that but if you hold shift and click and drag, you can select multiple nodes. If you zoom all the way out, you can accomplish this much easier.
My preferred method for doing something like this, however, is to add an EQ or compressor (anything with an output gain though) and use that gain as a volume controller. You could also do this in another order: automate your output gain on a plugin and you can still use the output volume on your track.
Another option would be to set up a bus for your output of the track you want to do this with, then apply your automation to the bus track and you can either use the volume on your actual track, or the send to the bus.
There's usually loads of ways to solve problems like this one, so it will really end up being about what you prefer to do.