I get the same feeling of momentary compulsion to exactly answer a greeting when confronted with two very common greetings in Thai: "Have you eaten rice yet?" and "Where are you going?"

To this day, I am still not entirely confident in how I should respond with to the prior.

In regards to the English "how are you?" greeting, think of it as a formulaic inquiry meant only to ensure there isn't anything absolutely horrible going on with you at that exact moment - anything lesser equates to "fine" or "I'm well, thanks."

More broadly, it is an appropriate situation to note anything out of the ordinary going on - "oh wow, I am so tired this afternoon!" etc to scope the ensuing situation. The greeting really is a question that equates to being asked "is there anything particularly out of the ordinary going with you right now I should know about that would impact us talking?" If there isn't, "I'm well, thanks."

(I know you know all this, but your comment got me musing on the topic.)