Hi Adel. In some sense I have made peace with QFT, so that random fields have become merely background thinking. I found, in particular, that although I could construct a random field equivalent for the quantized electromagnetic field, I could not construct a random field equivalent for quantized Dirac spinor fields, and I couldn't prove that it's not possible, so that I felt that I had to give up that line of thinking for now. I also gradually realized some parts of why the nature of the relationships that I could construct between random fields and quantum fields would not be convincing for physicists, but without enough clarity to be able to publish that realization.
Nonetheless, QFT can peacefully coexist with classical stochastic fields by taking QFT to be a signal analysis formalism, and taking the empiricist line that what the causes of the signals are is not so important insofar as they are inaccessible (if a cause isn't inaccessible, then it's a signal, so it can be analyzed, together with its relationships with other signals). If all our measurements are noisy, to the same extent, then signal analysis is relatively difficult and somewhat counterintuitive, with Hilbert spaces and noncommuting operators being a naturally useful mathematics for models of experimental apparatus. As a single sentence summary, state preparations in QFT are modulations of the vacuum state, and measurements identify how similar a given state is to a reference modulation (or, for a mixed state, to a collection of reference modulations).
I regret to say, Adel, that I can't make much contact with the paper that you link to. I feel that you've fed more assumptions into your modeling than you think you have, and that unpicking those assumptions is something that it may take you a while to do. In particular, I note that a collection of points randomly chosen is not a simple thing, since the choice of a random process to provide those choices already encodes a lot of information; saying something like "of course it should be Gaussian", for example, puts you on a direct course for something like a quantized harmonic oscillator. As another possible point of departure, although it sadly introduces much more complexity, it might help if you think carefully about how your ideas would apply in Minkowski space, insofar as working in a more general setting is one way to help one realize where unacknowledged assumptions have crept in.