If climate science were a highly competitive area where a low percentage of grant proposals get funding, things would be different. Then, to paraphrase your words: “Getting results that have an impact would be very, very, important”. An “impact” would be definitive conclusions about whether the MWP, the LIA, and the CWP penetrated south to Antarctica. If various proxies disagree (as seems likely), which ones should we believe and why? Other researchers need access to all of the Law Dome data so that they can test their hypotheses about why proxies may disagree. .

The p value is the probability based on sampling procedures that the null hypothesis might be able to arrived at observed results. The choice of experimental design, sampling procedures, and null hypothesis is very important to not arrive an apparent statistical rejection of null hypothesis that lacks meaningful scientific value. The convention of using the null hypothesis and p values is already quite imperfect. When procedures includes a step to select samples based on the dependent data, the impact on probabilities is ill-defined.