How successful would you say has been the idea to derive QM from number theory?
They remain still many open mathematical questions to proceed. But the point is that if comp is correct (and comp is the favorite hypothesis about the observer for many many-worlders) then we *have to* derive QM from comp, independently of the difficulty of the task. It makes also comp Popper falsifiable: just derive QM from comp, and then compare to empirical QM.
What proportion of physicists are aware of this idea?
I don't know. In general physicists take the existence of the universe for granted. Also most dislikes the idea that physics is not "fundamental". But some understands the proof. Other are open to the idea that QM comes from numbers, because there are evidences from number theory itself (relation between knot theory, quantum field and prime numbers for example: see http://www.maths.ex.ac.uk/~mwatkins/zeta/index.htm I am pretty sure that "materialism" will be considered tomorrow like "vitalism" today: a sort of empty hypothesis, if not a superstition.
How does it relate to the Russell Standish derivation of QM?
It does not presuppose space, time. It confronts the mind body problem, and also I still believe Russell presuppose the linearity of the evolution.