Rebuttal of a Rebuttal

First of all, thanks for the detailed criticism.
So let's start. You criticize my statement that Existence exists is a tautology and therefore meaningless. You then say that an undebated starting point is a solid foundation for further investigation.

Well, the thing is this: "Existence Exists" can be seen in two ways: IF taken as a logical statement "Existence exists" has the same truth value as "A is A" or "Swifty monselers monsel swiftily". As such it is tautological and true by definition but without much use for further study. IF taken as meaning "There is existence apart from myself", (which is how Rand meant it) it is a mere statement of belief with no further proof given. This IS a good assumption that does serve well as a starting point. However, it's an assumption, not a logical necessity nor self-evident as the tautological statement. I accept it as a very good assumption, but refrain from giving it any higher status.
I do not believe that I'm in the Matrix, but I think it can't be ruled out as a possibility. I have yet to see an argument that shows this is impossible. (As a sidenote, I've been giving the example of being a computer simulation before "The Matrix" was made and I'm thankful for the Matrix movie because it saves me a lot of explaination time).

1.2 Free Will

How you come to the conclusion that I haven't read Gödel, Escher, Bach is beyond me. Also I wonder how Hofstadter's strange loops can give rise to real free will in a deterministic system. Practical unpredictability, yes. Self-reference, which may give insight into how consciousness works, yes. But real (and not just epistemic) free will, ... you'll have to elaborate on that. If you really have something here, I'd be thrilled to know it.

2. Ethics

Let's go straight to the source. Ayn Rand states in "The Objectivist Ethics" that it's the built-in goal of any living being to individually survive:
"On the physical level, the functions of all living organism, from the simplest to the most complex - from the nutritive function in the single cell of an anoeba to the blood circulation in the body of a man are actions generated by the organism itself and directed to a single goal: the maintenance of the organism's life."
VOS, page 16

I don't think you can state it any clearer than that. From this, she reasons that man, having free will instead of automatically functioning instincts, has to find out about this and then act on it.

The objectivity of her morality stems from the claim that what her morality entails is in harmony with what the goal of life is for ANY living entity. So if I go ahead and show how this is not the real goal of life in animals, but just a secondary one by giving an example, the argument that I'm then talking about other animals, not humans, doesn't hold water. Here's another example: The peacock. How on earth did that strange creature evolve if all life is about is survival? It has a long bright tail which shows it to predators and handicaps it when it tries to run from them and costs expensive energy to maintain. That creature shouldn't exist. Darwin once said that he got sick whenever he saw a peacock. His solution was that animals aim at successful procreation (which makes existence during the very act of it necessary, of course). So if you have to pick a single goal as an organism, it clearly is procreation, not individual survival.

It's not the case that if you don't choose life as your ultimate value, you have to choose death as your ultimate (the nice "go commit suicide"-argument). You can still have life as a lesser value, still work hard at survival and yet risk it for other things of higher value, like procreation. The animal world is full of examples of this.
If you have to take "survival" as a primary goal, it's genetic survival. And this goal makes it worthwhile to sacrifice individual survival to success in procreation, which is why you can see it throughout life.

How an arbitrary choice of absolute value bridges the is-ought gap is something that needs a lot more explaination.

Albert Ellis

Well, Albert Ellis stated clearly (and repeatedly throughout several of his books like "The myth of self-esteem") that a belief in something like self-worth itself leads to mental problems. It leads you to having to prove your own worth to yourself all the time, to thinking of yourself as above all others when you "do good" and subhuman when you don't, and keeps you in constant anxiety no matter what your current grade is on your scale.
Ellis disagrees with Objectivism decisively, he even wrote a book called "Is Objectivism a Religion" as referenced in that very Wikipedia article you mentioned before criticizing me of not bothering to research the ideas I am criticizing.