Eckard,
Reading your -- "Dirac possibly ... believed that this concept of the probability amplitude is perhaps the most fundamental concept of quantum theory? If my doubt is justified, then it is even more fundamental" --
I took the "it" to refer to Dirac's opinion about the probability amplitude. Hence my comment in the context of the more fundamental R-F theorem.
I see now (and somewhat surprised by your accompanying doubt), that your "it" here "referred to a much more radical doubt that I tried to express in my essay."
Please, what is that radical doubt? I did not see such a thought in your essay; perhaps I am a less-doubting radical?
Thus: there is so much that I agree with in your essay, I truly wonder where your doubt arises. Are you referring to this: "Therefore, some putative pillars of science are suspected to be just semi-fundamental constructs on a shaky basis. Judge yourself." ??
I (see my essay) would strengthen you claim to this (and without doubt): "Some supposed pillars of science are false. Judge for yourself. See how far we advance by rejecting the ubiquitous and unqualified (but primitive) notion of REALISM in physics (it is NAIVE REALISM). That is: simply replace NAIVE REALISM by TRUE REALISM* (the insistence that some existents may change interactively), and see quantum theory derived classically." [Then, relatedly, there is Bell's theorem; as in my essay's Appendix!]
* With such true realism known to me since the age of two, with a photo for proof (me with my rail-spike-for-a-hammer beside a newly-fitted but now smashed porcelain toilet bowl), me having imitated the plumber who (10 minutes earlier) had gently tapped the bowl into the fresh cement with his own steel hammer! dink-dink-dink, I can still hear it! [Me, as ever, trying to make sure things are right ... kaboom.]
This story for you: some light-relief as to why you should, today,** NOT be tense and NOT harbour any doubt, radical or otherwise!
** Given your own analyses, with my essay.
PS: You say, "There is one reality." In agreement, I add, "Reality makes sense and we can understand it." Against Bell, I add, "Correlated tests on correlated things produce correlated results without mystery." To you, I say, "Only the impossible is impossible."
HTH; and loving your very deep essay,
Gordon Watson
More realistic fundamentals: quantum theory from one premiss.