Of course I really want to fight against this crap -I still have difficulty to say that it is a disease because I don't think so- and all together ! It is good to follow the same way, we can share our results each other.
As you say, I think that the important thing is not the number of sessions but the length of them. Like you, I stay under about at least 10 min, not because of a big reflection but it is a bit annoying and seems lengthy enough.
Regarding the drops which run down the face I think it is just the water, the sweat in a very small amount, because they are not salted at all.
I don't think that it is a wrong thing to let lips getting wet during the treatment -or I have maybe misunderstood ?- because it would be as beeing in the 'desert', very hot and dry. The importance of this steam treatment that it brings precisely heat and humidity.