Canonical Transformations and the Theory of Everything

Everything is described by the laws of physics - and if this is not so, we have to change the laws of physics. That is the fundamental approach of physical research and as the final goal, physicists want to describe not less than everything. In practice this always comes down to finding the right set of equations to be applied in the right mathematical formalism. Concerning different set of equations, the universe seems to be pretty creative: Mechanics is governed by ordinary differential equations, Electromagnetism by partial differential equations and Quantum Mechanics even uses operator-equations in infinitely dimensional Hilbert-spaces. Things look differently when it comes to the right formalism: In fact, there is actually not much more than Hamiltonian (Quantum-)Mechanics. You may ask - so what? - if physicists search for a theory of everything - and for everything there is a Hamiltonian, then they are on a good way. Well kind of. Indeed, most if not all of current physical research is looking for the right Hamiltonian, and of course clever methods to solve it. There is a Hamiltonian for the Standard-Model, and people are working hard to extend it in order to treat Supersymmetry, Quantum Gravity, String Theory etc. etc. What puzzles me is now the following: In principal you can always transform your set of coordinates, e.g. it should not matter if you define the origin of your coordinate system to be here on my desk or at any other point in the universe. In general, besides choosing the point of origin, there are many other, more complicated and sometimes even time-dependent changes of coordinates, and within Hamiltonian Mechanics they are all equivalent and called canonical transformations. Among all possible canonical transformations there is always a really special one, namely the transformation to the solution of the Hamiltonian equations of motion. In this very special set of coordinates, the Hamiltonian is always equal to zero! Surprised? You sure should be. I just told you that many physicists are looking for the right Hamiltonian description of the universe and here is the solution: It is zero! - So all the work for nothing? - Well, certainly not, there still remains the question of the Canonical transformation - and about that, I honestly do not know anything. But my real point is: Somehow we all know that there is one preferred set of coordinates, namely space and time. We are free to move in space and we are forced to move forward in time. This very subjective experience contradicts Hamiltonian Mechanics  where any choice of coordinates is equivalent. Consequently, I would guess that in order to explain the true foundations of the world surrounding us we have to go beyond Hamiltonian theory. In what sense - I really do not have any idea - but I would be very happy to hear from anyone who has some!