Dear Eckard,
I totally agree with the first sentence of your abstract "Some seemingly mysterious interpretations of mathematics by physicists are just unwarranted" and most of what you are writing afterwards. My longstanding interest is to recognize and possibly expand the right mathematics appropriate to a seemingly paradoxal subject. I did it by using number theory for explaining the non-orthodox statistics one find in the so-called 1/f noise that you may know because you worked in signal processing. I do it now by using group concepts for understanding the deep nature of quantum paradoxes such as EPR.
I like that you put the development of mathematics in an historic perspective on p.2 and afterwards and criticize the false ideas that have appeared and have been corrected by the appropriate maths.
I disagree with "physics must be fully consistent with the premise of only one causally connected real world", where this requirement (that reminds the requirement of the preexistence of a space-time) comes from? For example, quantum theory don't need space-time and is acausal.
Finally, I enjoyed reading you and I hope you take the time to read my essay as well.
Best,
Michel