Daniel:
There are too many things here to deal with in depth, but briefly:
Point 1. I’m aware that the word “random” is used in many different ways, in various sciences and in everyday speech. I don’t want to make a big deal about the term itself, lest we get caught up in the technical details of what physicists mean by randomness, what neo-Darwinism means by randomness, etc. and get lost in a morass. I’m quite happy to stick with a more general term like “chance.” When we say that life originated by “chance”, we normally mean that it did not originate either by deterministic necessity or by design, but by a concatenation of unplanned events that easily could have been other than they were. The conception of those who think it happened by chance is that it came down to the equivalent of a roll of the dice (even if thousands of times repeated rolls) whether or not Earth would have any life at all. That usage should be intelligible to lay Christians and Christian scientists alike.
Point 2. I agree with you that the question of the origin of life isn’t isolated from other questions, but if you recall, you asked me to focus for the time being on the origin of life. 
Further, I said that it seemed to me that the logic of some TE arguments about evolution carried over into their conclusions about the origin of life, so I’m making no artificial separation. Finally, from a theological point of view, I’m just as interested in the question of whether and how God acted in evolution as I am in the question of whether and how he acted in the origin of life. (And when I’ve asked questions about God’s role in evolution, as opposed to origin of life, I’ve got the same theological runaround from most TE leaders.)
Point 3. I’m not saying that one can’t have a theological discussion about anti-matter etc. as you have mentioned. It might be that the origin of the balance of matter and anti-matter is something that should be attributed to divine special creation rather than to any natural law. I take no stand on that. If you tell me that this is a live intellectual question among religious physicists, I will take your word for it. But I’m trying to focus on the topics which people in these debates have more generally discussed, i.e., the evolutionary process, and the origin of life. These make sense as examples for everyday folks, as Christians read in their Bibles about the origin of “kinds” and of the first life (or at least of the first things that are called living by the Bible, i.e., birds and sea creatures), and of the origin of man, whereas they don’t read about the origin of anti-matter or black holes or quasars or other things whose existence wasn’t even suspected by people of Biblical times. So I’m not trying to avoid a general question by focusing only on isolated examples; rather, I’m focusing on examples which are of the most interest to people involved in the discussions.
ID writers rarely speak of “purpose” (because the term is ambiguous), but they have written at great length trying to characterize design and design inferences. Dembski’s early books took great pains in this regard, Behe has much to say about it in Darwin’s Black Box and elsewhere, Meyer and others have provided lengthy discussions.
I already indicated that for ID people “randomness” might be one of the natural means God uses to actualize a design, but randomness doesn’t replace design itself. My concern is that sometimes TEs write as if (they may not mean to convey it, but it sounds like it) randomness is sufficient instead of design.
Finally, no my arguments aren’t primarily Biblical or theological. I think there are plenty of good scientific and philosophical reasons for doubting that either evolution or the origin of life proceed by the means frequently envisioned. That does not mean, of course, that no evolution has occurred, but the why and how are in my view much more uncertain than some people would have us believe.