I think you partly nailed it with
I am experiencing existence. We experience the process of experiencing. Then I think you're wrong when you say consciousness can't be measured. It probably can.
What we have here is a system receiving inputs, observing how it reorganises itself under these inputs and influencing this reorganisation based on the results of previous experiences. For sure we can measure that a system doesn't merely learn but influences its own learning process depending on previous learning experiences. This may be what allows us to project knowledge from a domain to another, and what allows us to produce artificial knowledge by learning from others. We produce arbitrary connections through memory / continuity of experience and communication. This would provide a basis and a reason for language and societies.
What we miss here is a self-sense, and Koch hints at it IMHO. Integration may be key. I'd say dependency to make it clearer, state dependency. Two linked states where one reflects exactly the value or the other could effectively be labeled as one. They would feel as one, too. What I define as "me" is what has direct influence on me and what I have direct influence on. There isn't a clear boundary though. This definition still has a problem as we define me as what is related to me, so maybe a better definition could be found by taking it by the other end and defining as feeling like an individual "me" every intergrated conscious instance significantly disconnected from the others. A fragmented big abstract me, for short.
If we define consciousness this way it exists in the positivist framework (which satisfies me a lot) and yet it can exist in more exotic frameworks too, like the ones where one can experience that everything ultimately depends on everything when seen under the right scale, and that the sense of self can be extended to everything.
I'm still unable to devise a clear experiment to prove consciousness defined this way though, maybe because I'm plain wrong and it's impossible !