and possibly will have to be...

That begs the question of whether or not it is correct if taken to an extreme -- and in my view, it has been taken to that limit.

I would also suggest that while this statement reflects the current reality:
"...Imagine General X coming to your AO, and when he asks how you know your program is working, you say, "I just feel it in my bones, General." Now, he may be a great guy, and he may trust you implicitly. But he has a boss who doesn't know you from Adam, and eventually, "Don't worry, LTC A feels in his bones things are going well," will no longer serve as justification."
the Army did not always operate like that and I, old, though I be, strongly question three things in this admittedly current mode:

1. If I'm LTC A, the General's boss should know I'm trustworthy regardless of whether he knows me or not -- if he doesn't know that, then I suggest there's a systemic problem in how I got to be a LTC that probably needs to be addressed. An Army has to operate on trust and not who one knows, the pipeline will not always give you people you've worked with before. That process works (albeit very poorly and unethically) in peacetime and in little wars like these, it will not work in a major war, too many replacements.

2. If I'm LTC A and answer my boss with a statement like that, I don't deserve his or anyone else's trust and I probably am not going to be able to produce a meaningful set of numbers to change that correct assessment. conversely, if a set of numbers assuage my boss's boss angst, I'd worry about him...

3. If I'm sensibly fulfilling my reporting requirements, the General should know how I'm doing without asking. If I'm not then I'm way wrong, if I am and he does not; who's wrong?

The issue, as I said, is not totally echewing numbers, it is that metrics be properly selected -- and in my observation, post 1962 when the numbers syndrome was introduced throughout DoD without regard to validity of effort, that has been rarely been done well. I also said that the danger of metrics being an end in themselves is quite real and can be dangerously misleading. That, to me is the crux of the issue.

You also say:
So I would suggest formulating metrics for every aspect of your COIN program, both as an inherently worthwhile exercise, and as a protective measure against the business managers who lurk in every headquarters.
I'd change the first part of that to read; "Formulating sensible and pertinent metrics for those aspects of your COIN program where they can truly add value is a worthwhile exercise and is just common sense."

I'd also suggest that the latter part of your paragraph has become the real reason for most, not all, metrics -- and we can continue to disagree on both the ethical and the military value of that.