Would love to see the paper as well. Everything you said about antioxidants is true and I have equity in a company that has spent millions on researching antioxidants at multiple universities, on two continents. Most benefits that companies make claims on are only seen after ingesting impossible to eat"natural" quantities of the antioxidants.
Even more interesting, the heavy metal claims. Heavy metals are generally leeched from the soil and to conduct a test such as this you need two very different plots of land. If the heavy metals were in the solutions applied to the conventionally grown crops, then it would be pretty easy to know where they came from and alert the governing agencies. Therefore, they came from the soil.
Although there are no real enforced standards for organic in US, most private companies that set the standards have some specifications for the soil. If you were to convert a field from conventional to organic, the general rules state that the field needs to become farrow and tested for at least 7 years. In theory this does gets rid of chemical pesticides, but there are no major studies to prove it and there is no impact on residual heavy metals.
And as someone that grew up in the produce, food and beverage business I will say that just because something is labeled organic, it does not mean it is organic. It certainly does not mean that the private company they chose to "inspect" there farms followed through with all of their privately chosen standards. My family's company has caught more than a few competitors and business partners cheating the system, selling organic product in quantities that the industry knows the company cannot meet in terms of production.
General rule of thumb for buying organic: is it smaller and more "meh" looking than the conventional fruit or vegetable... it's probably organic. If it's processed and packaged... it's anyone's guess. There certainly is no governing body trying to enforce standards. After all, regulations would only cut the profit margins for the already established major organic players.