Experimental Test of E=mc2?

Let us seek experimental test for the cornerstone of modern physics Einstein's $E=mc^2$. We find on MIT News 2005: E=mc2 passes tough MIT test (as a celebration to Einstein's Annu Mirabilis 1905):

• MIT physicists report the most precise direct test yet of Einstein's most famous equation, E=mc2. And, yes, Einstein still rules. 
• The team found that the formula predicting that energy and mass are equivalent is correct to an incredible accuracy of better than one part in a million. That's 55 times more precise than the best previous test. Team member prof. Pritchard says:
• "In spite of widespread acceptance of this equation as gospel, we should remember that it is a theory. It can be trusted only to the extent that it is tested with experiments....If this equation were found to be even slightly incorrect, the impact would be enormous -- given the degree to which [it] is woven into the theoretical fabric of modern physics and everyday applications such as global positioning systems."
• (We meet here the common claim by physicists that GPS relies on relativity theory ($E=mc^2$), which is not the reason GPS works). 
• The mass loss was obtained at MIT by measuring the difference between the mass of the nucleus before the emission of a gamma ray and after. 
• Pritchard informs: "Determining the mass difference requires the individual masses to be measured with the incredible accuracy of one part in 100 billion -- equivalent to measuring the distance from Boston to Los Angeles to within the width of a human hair! This doesn't mean it has been proven to be completely correct. Future physicists will undoubtedly subject it to even more precise tests because more accurate checks imply that our theory of the world is in fact more and more complete."

Ok, detection of the mass loss required a measurement accuracy of one part in a billion (0.000000001) since the measurement was made on a single nucleus emitting a gamma ray. To measure mass defect it would seem to be better to involve a more easily measurable bulk of mass. To measure the mass/weight of a pile of sand, it would be senseless to measure the mass/weight of each grain of sand and then add up. It would be more sensible to seek to measure the mass defect in some nuclear reaction since it would require less precision, like the mass defect in an atomic bomb explosion...

In any case Pritchard admits that this does not suffice to be sure that $E=mc^2$ is exactly correct. And this is needed, because if $E=mc^2$ is not exactly correct, then the floor of modern physics collapses. If $E=mc^2$ is only approximately correct, then an abyss of questions opens: What is then missing? In my case, how much can I rely on $E=mc^2$? Which mass cannot be converted to energy and vice versa?  The suspicion from previous posts comes back again: Is $E=mc^2$ just and agreement, and as such always exactly correct, like the statement that there are 100 centimetres on a meter, for which experimental verification would be met with laugh.

A detailed inspection of many tests supporting the suspicion is given in Mass-energy equivalence not experimentally verified with punch line 

• It was not a verification of E = mc2, but just another experiment to deduce the mass of the neutron. To date, we have not measured the true mass of the neutron to any degree of accuracy; we only have a deduced estimate of the neutron mass based on the mass-energy equivalence of E = mc2.

We understand that the mass defect of the neutron, used as a proof of the correctness of $E=mc^2$, in fact is computed from $E=mc^2$ because the true mass of the neutron cannot be measured with enough accuracy. And so the mass defect is an agreement and not verified physical fact.