There is much wrong here, but I will try to focus on your bizarre inability to recognize the vast, qualitative difference between prediction and norm.
Only in a classic, philosophical sense is the second one "invalid". In the future, they will be considered equivalent by the bulk of academia, for all practical intents and purposes, if my predictions are to be true.
By "classic, philosophical sense," you mean the sense used in logic in all its various academic settings, including mathematics, computer science, etc., I assume. The fact is that, so long as the second argument is (as Tassman and you seem to think) an inductive argument, then its conclusion is merely probable and not certain, given the truth of its premises -- and the degree of probability varies with the strength of the argument. Surely, any deep thinker can see the difference between an argument which establishes the truth of its conclusion and one which merely establishes the probability.
But this is a nitpick. Let's move on to the meat.
Here is a more realistic way to think about it:
I want the hut to be habitable.
The hut will require heating in order be habitable.
If I do not heat the hut, others in the future will recognize my mistake, and will be more likely to heat their own huts.
A completely different argument, and one which is arguably weaker. The causal connection between my failure at one task and the behavior of others at that same task is so weak as to be laughable. The argument now depends that others are observing my behavior, see that the hut never attained habitability, attribute that fact to the lack of heat, later acquired a hut that also lacked heat and adjusted their behavior so that they heated the hut in those situations.
But, of course, we already took for granted that the agent knew the hut required heating in order to be habitable. This is why the classical argument concludes that, so long as the agent is acting rationally (and so long as he wants the hut to be habitable), then he ought to heat it. This information is, presumably, available to all these other hut-owning agents you claim are learning from my mistake, but why they should bother watching me is a mystery. Every rational person recognizes that he ought to do that which is necessary to attain his ends. These other guys don't have to learn it from me.
Your restated argument is honestly a large step in the wrong direction.
I have a choice, today, of being recognized as a person wise enough to heat their own hut, or dumb enough to not do so. But, that choice becomes more likely to take one side (heating the hut), than the other, over time.
Therefore, I ought to heat the hut, and I MOST LIKELY will heat the hut.
It is perhaps the case that you will most likely heat the hut, but that does not mean the statement "I most likely will heat the hut" does all the work of the statement "I ought to heat the hut" --- not even if (and this is a big if) they were derivable in the same circumstances.
The fact is that persons are imperfectly rational. This was, of course, the point of the gambler's fallacy example which you so bizarrely misread (a sequence of coin flips are independent events? Thanks for that fact!). We are so evolved that there are certain fallacies of practical and theoretical reasoning that we tend to make. Based on past observations of human behavior, together with elementary arguments of practicality, one can sometimes conclude the following:
Although Bob should not, in this situation, do X, he nonetheless will probably do X.
I'm sure you've said something like this before, perhaps watching a favorite sports team whose coach has a history of using a certain kind of bad strategy.
Now, if your account was right and people are evolving so rapidly that they are overcoming the apparent sub-optimal design of their own brains (perhaps in a grand Lamarckian way), then the truth of the ought statement will make the truth of the prediction probable over time. Frankly, I think that's a fairly utopian view of the future progress of human reasoning, but never mind. Even if that is so, there is still a difference between the ought statement, which expresses that the particular action is, in this case, not in the agent's interests, and the prediction, which expresses merely that the particular action is one which the agent tends to choose to do.
In sum:
(1) You have given no reason to believe that, "You ought to do X," is evidence that the probability of doing X is increasing over time, aside from wishful thinking.
(2) You have given no reason to believe that, even if the claim in (1) is true, the distinction between what is rationally required and what is probable is unimportant. You pretend that prediction can supplant evaluation.