I wonder if you would apply the same criticism to so-called "derivations" of quantum theory from information theoretic principles, specifically those which work within the environment of general probabilistic theories. For example:

http://arxiv.org/abs/1011.6451 ; http://arxiv.org/abs/1004.1483 ; http://arxiv.org/abs/quantph/0101012

The above links, despite having perhaps overly strong titles, are fairly clear about what assumptions are made, and what is derived. These assumptions are more than simply uncertainty and robust reproducibility: e.g. one assumption that is made by all the above links is that any two pure states are linked by a reversible transformation (in the first link, a slightly modified version of this is assumed). Of course, "pure state" and "reversible transformation" are well-defined concepts within the general probabilistic framework which generalize the meaning of the terms in quantum theory.

Since this research is closely related to my PhD, I feel compelled to give an answer your questions about uncertainty relations and complex numbers in this context. General probabilistic theories provide an abstracted formalism for discussing experiments in terms of measurement choices and outcomes. Essentially any physical theory that predicts probabilities for experimental outcomes (a "prediction calculus" if you like) occupies a place within that formalism, including the complex Hilbert space paradigm of quantum theory. The idea is to whittle down, by means of minimal reasonabe assumptions, the full class of general probabilistic theories until one ends up with the theory that corresponds to quantum theory. What you then have is a prediction calculus equivalent to that of complex Hilbert space quantum theory. In short, complex numbers aren't directly derived from the assumptions; rather, they can be seen simply as part of a less intuitive representation of the same prediction calculus. Uncertainty relations can of course be deduced from the general probabilistic theory if desired, but since they are not part of the actual postulates of quantum theory, there hasn't been much point in doing so. It bears mentioning that this "whittling down process" has so far been achieved only for finite-dimensional quantum theory, as far as I'm aware, although there is work being done on the infinite-dimensional case.