It might help to set out exactly how you believe "drawing twice" manifests itself in each of your examples.
At -3 Karma I'm not too eager to make that effort. But a bit more details might be helpful.
Let's take the doomsday argument (the sleeping beauty is a bit more complex). The argument is that there's a 2/3 probability to be one of the last 2/3 of humans, therefore doom is immanent (or imminent, I can never remember which is which).
In this argument you are "drawing twice". The first drawing is the drawing to identify yourself, the second drawing is drawing yourself out of all humans. However, you are in fact only "drawn" once in identifying yourself through your conciousness. There is nobody there to draw you a second time. Therfore the argument is wrong. If we remove the first drawing, leaving only the second one, The probability is of course 2/3 that we will draw some human out of the last 2/3. But that might be Zzydrh the star explorer, that single drawing will be you only with the probability 1 to the number of humans that will have existed.
If on the other hand we remove the second drawing, leaving only the first, you cannot ask what human you probably are, because we have only drawn once and called that one human "you", i.e. each and every human to exist draws only himself out of the urn. None is drawn twice and none is not drawn. Imagine a line of humans each drawing one marble. Now ask the first one in line after he has drawn what the probability was that he drew the first marble. If you by any means identify one of the humans as "you", you have made a second drawing, which in real life doesn't happen.
As I understand it, in your presentation the doomsday argument corresponds to some of the human-marbles being coloured red, and then asking the first marble in the line what the probability that he was coloured red is: to me the problem appears to be directing questions at samples from probability spaces. I'm now perilously close to just giving a careless analysis of the doomsday argument though.
I think you may have attached the phrase "second drawing" to a useful concept, but it's not entirely clear what that is. If you can find a lucid explanation, then we might learn something.
Suppose there are ten white marbles in an urn. If I draw one of them, what was the probability that I would draw that specific one? If your answer is 1/10 you've just drawn twice. Once to determine the identity of the marble and once to draw it out of the others. If you only draw once, than "that specific one" simply refers to the marble that you drew making the "probability" 1. You cannot follow the identity back after you drew it, because drawing it was the cause for attributing an identity to it. Identity in this sense is in the map not the territory.
This is the same mistake that sleeping beauty makes. She draws once to determine her own identity and once again to draw out of the other "possibilities". The same mistake is behind the doomsday argument. You draw once to determine your own identity and once again to draw yourself out of all the humans. There is no 2/3 probability that Ogh the neanderthal was one of the last 2/3 of all humans. As soon as you say "But I am not Ogh the neanderthal" you are drawing a second time. Otherwise all marbles are white, i.e. all humans are conscious.