And my view, as not very resident interested skeptic.
you will not find any null hypothesis in a form that can be proved. LENR rests at its heart on the problematic idea that somehow nuclear reactions can proceed without unstable products or high energy particles (both of which can be very easily detected). Attempts to detect either of these have proven difficult and always in the margin of possible error or non-replicable.
For me though, the bottom line is that after 40 years of effort and a lot of experiments of many different kinds, nothing sticks experimentally.
As you state the heart of the problem is that LENR proceeds without the high energy products produced by radioactive decay or a nuclear reaction stimulated by a high energy collision.
Since heart of the problem is true, the detection methods you mention will always show far less unstable products and high energy particles than predicted given that only a high energy collisions can cause nuclear reaction. But, nuclear reactions can occur without a high energy collision. That leaves one to prove or disprove reaction based on transmutation. Basically, one must prove or disprove the reaction like one should any reactions: by mass balance and stoichiometry.
You can prove cold fusion to yourself with a little math, just check the null hypothesis using the reference I provided above. If there is no reaction there is no transmutation and no stoichiometry. The data provided by Santilli is mass spectroscopy in gas which is accurate to 3 ppm. The result of the math is 29876 ppm of Deuterium and 4805 ppm of Oxygen is disappear while 9061 ppm of Nitrogen and 9793 ppm of hydrogen appear. There are no unaccounted changes. You can check the precision of the reaction by dividing each coefficient by 9061, the amount of nitrogen. The coefficients are slightly off because there is a secondary reaction. Once the secondary reaction is solved, the accountability is very close to the 3 ppm expected by the accuracy of mass spectrometry.
The reaction is not a single elementary reaction or based on collision of two atoms. Rather, there is a nuclear active cluster where a cascade of elementary reactions occurs. The sum of reactions produces the overall reaction equation above. The fact that "the heart of the problem" is true does not prove the reaction did not happen. Rather the Gibbs equation indicates the energy produced by reaction comes in two forms heat and entropy as a function of temperature. The simple explanation here is that the more fragmented the quanta of energy produced by reaction becomes the more entropy is present rather than heat. Further entropy is not disorder but rather energy to mass conversion, hence the connection between relative mass(velocity) and temperature.
There are many examples of this type of cold fusion which have been reproduced many times. Gas produced by cold fusion is commercially available.
I have tried to show how wrong your views are and to show you where we need you to focus to realize cold fusion as an energy source. If the next step were easy, I would have done it already.