By the way, your complaint here...

To stick with the analogy of relativity, great efforts have been made there to ensure that all important physical formulas are Lorentz-invariant, i.e. do not depend on these artificial coordinate system. In an important sense the system does not depend on your coordinates, although for actual calculations (on a computer or something) such coordinates are needed. So while (General) Relativity indeed satisfies the last line you gave, it also explains exactly how (un)necessary such coordinate systems are, and explains exactly what can be expected to be shown without choosing a coordinate system.

Back to RQM. Here this important explanation of which observables are still independent of the observer(/initial frame) and which formulas are universal are painfully absent

..is echoed by no less than Jaynes:-

The title is taken from a passage of Jaynes [2], presenting the current quantum mechanical formalism as not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature – all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble

http://arxiv.org/abs/1206.6024