As another mentioned, exercise can do it. I find running to be meditative. Other than following the path (and sometimes just running) my mind is free to do whatever. No distractions like computers and TV. I usually run without music as well.

I also took up Brazilian jiu jitsu this year and I'm finding it helpful in another way. I'm not very good at it, so I have to stay focused during class and rolling trying to connect the dots. And it's sufficiently physically exhausting that once I'm done I'm ready to eat and then pass out. The next morning in feeling the soreness of my worn out muscles. Different but not totally unlike the hangovers described. The major difference being a sense of accomplishment and improvement letting me know that what I'm doing is worth the effort.

Meditation works for me. I am relatively new to it (few months) but have found what I was looking for simply by understanding that I am not my thoughts, that without them I still exist. I began to understand that thoughts are a lot like weather, or like throwing a rock in a pond. For me, I was able to move from that realization to being able to not get swept up in thoughts. This gives me the clarity that I am assuming is similar to what the author found during his hangover. The point for me is understanding that the mind and its processes are a tool. The ability to choose when to use it is freedom.

Some people may also find this through religion or (my opinion) more directly through spiritual practice outside of the framework of a given religion.

Others may use psychedelics. Medical marijuana has been helpful for me in some instances, but I tend to rely too much on it and as a personal choice now try to limit my use. I can understand how alcohol could lead a person to this but there are many healthier alternatives. I could see a person drinking themselves to death before they find it.