The latest reason for not saying what you mean by likeness is that you don't want to do what it would take. While I can understand your reluctance to go there, it does not make the problems created by the absence of any specifics about this likeness go away.

You say that doing so would take the scope of the discussion far beyond whether thought can be material or not. This is surprising: this likeness, and claims about what follows from it, are key premises to your argument, and so, surely, establishing what this likeness is and how it leads to your conclusion is central to addressing the question of whether thought can be material or not has been answered by your thesis?

Your assertion that this would be re-inventing the wheel does not seem to fit with your concern about the scope of the ensuing discussion, either - if it's all been worked out already,how come it hasn't been written up already in, say, the Stanford Encyclopedia of Philosophy, all packaged up and demanding little more of your time than some commentary (it is also implausible that if this wheel has already been invented, philosophers would still be about equally divided over the question - and yet they are.)

As it stands, your claim that the answer is already out there is yet another one made without justification, and any suggestion that skeptics of your bold claim should figure this out for themselves would amount to another form of burden shifting.

Examining your compromise, "two objects are alike if they are the same in some respect" seems to me to be a good definition of 'alike' (better than those in the couple of dictionaries I looked at, IMHO) and likewise, I have little to say about "more formally, we could say that A and B are alike if we can predicate X of both A and B. As a corollary, A and B are entirely un-alike if we cannot predicate anything of both A and B", except that we need some sort of restriction on appropriate predicates (I don't think it would be helpful to say that a horse is like a dogma on account of their English-language names both having five letters.)

With regard to your three questions: there's nothing wrong with 1, though the definition of 'like;' that you have just given is so broad as to give little or any guidance; 2 is both the one I think might be answered by information flow via CHOC and the one you have resolutely avoided addressing (you still have not even said whether or not my CHOC-mediated 'correspondence' is your 'likeness'), and at 3, we can equally ask whether said manner can be immaterial.

You go on to say that you don't think "the same" can be usefully (verbally) defined,which I find surprising, as philosophers seem to use the word 'identical' with great abandon - is that not more or less the same? I might get your point if you said which more-clear and less-clear words you are thinking of here.

After this you seem to abruptly switch topic, leaving me puzzled as to what you are driving at in the six paragraphs beginning "But, as a compromise..." Is there something missing? It feels as if there is.

The point of the alternative argument is not so much that you are stating the opposite of premise 6 (arguably what you have said, in various ways, is not quite the opposite), but that both of them depend on leaps of faith for which no justification has been given.

One other thing I am still curious about is whether your likeness is intrinsic to thoughts (I gave my reasons for doubting it could be in my first Dec. 14 post, beginning "We can continue with this line of thought...")