First. The heat problem was their own admission. They themselves admitted that no known thermodynamic mechanism could have removed that amount of heat quickly enough, so they had to propose extremely complex solutions involving esoteric, bizarre, convoluted new laws of physics that are not supported by any evidence whatsoever. Problems of this level of severity are, quite frankly, a deal-breaker.
Second. Accelerated nuclear decay is an extraordinary claim, the kind that would win a Nobel Prize if it had any merit, not least because it flies in the face of both theoretical considerations and experimental evidence. As such, it needs extraordinary evidence to support it, including studies from multiple independent teams. The only evidence that we have are four disputed studies of uncertain reliability at best from a single team.
This isn’t a biased “evolutionist” response either. There are other examples from mainstream science that suffer from exactly the same problems. One particularly famous example was Fleischmann & Pons’s 1988 announcement of cold nuclear fusion. Other teams were unable to replicate it, and it’s now regarded by the scientific community as erroneous. This level of scrutiny is standard practice in science, and researchers are expected to address objections to their reviewers’ satisfaction, not try to argue their way past them.
Third. Even if these studies could be shown to have some merit, it is never made clear exactly how they are supposed to demonstrate accelerated nuclear decay. It is inferred solely from the fact that they can’t fit the evidence into six thousand years any other way.
Fourth. We need to ask ourselves why would God have gone to the trouble of miraculously accelerating nuclear decay in the first place and putting an extraordinary cooling mechanism in place to remove the heat? The only result of doing so would have been to make the earth look a whole lot older than it actually is. All they’ve managed to do is to propose a convoluted new take on the Omphalos hypothesis.
Fifth. The paper you cite merely shows that one event at Fenton Hill happened more recently than certain other studies suggested. There could be any number of explanations for the discrepancy, and further research may well shed some light on this. However, it places no maximum constraint whatsoever on the overall age of the earth, and fails to account for the numerous other studies elsewhere that place minimum constraints on the age of the earth far, far in excess of six thousand years.