The fact that you have outlined these steps in detail tells me that you are very cognizant of a thought process that you believe is happening (and it very well may be happening). Even, for instance, if you did drink one night, and did not get depressed, you would be expecting the impending depression/ anxiety, and the tension from anticipation alone would probably put you in a similar state. My point is to realize that part of it is happening "naturally," and part of it is a self-fulfilling prophecy.
Staying engaged is indeed a good way to cope with the situation. But in my opinion, a better way would be to not try to avoid or stop the chain of events from happening. When you let the feelings of depression/ fatigue/ anxiety/ panic to surface and even envelop you, you shine a light on them and slowly they become less scary and less intense; and at this point they are just annoying. I know when they are intense this can seem impossible, but it becomes easier with repetition and practice. Practice, practice, practice.
If you are drinking every day or close to it, or you feel that you are dependent on alcohol, then that is a different situation, but I am assuming you only drink within a normal range.
It would be easier for me to just tell you to avoid drinking, just like some people avoid caffeine, but I think that's a bad way to cope with anxiety. The solution I think lies in convincing yourself that you can get a buzz without this chain reaction. It won't happen over night, but if you keep letting the symptoms come when you start drinking they will gradually lose importance and intensity, until they are gone.