I'm wondering why the calibration constant shift peaks at a maximum D/Pd loading of 0.94
Short answer...no enough knowledge available to know.
First, the peak being at 0.94 may be a result of the sample size and the binning method used to make the histogram, i.e. a mathematical artifact. D/Pd = 1.0 is a 'magic number', since at that point all octahedral holes of the Pd lattice are filled with a D, so the max may actually be closer to 1.0. Need more data....
Second, under the assumption that the absorption process creates a 'special active state' (SAS) precursor, and that that may require a certain number of dislocations + superabundant vacancies (or the probability of forming the SAS is proportional to the number of acceptable surface defects), the ~0.94 number may simply be the point where the probability of forming the SAS has now reached a high enough level to be noticeable in these experiments, but some random variation around that is to be expected, since the process is not being well-controlled at this time (otherwise the CFers would have the level of reproducibility needed to claim 'full' repro.). Also one needs to remember that attaining these high loadings is not an instantaneous process. It usually requires some cook time (i.e. an induction period). So the .94 number might change is a different loading protocol was used. McKubre did a very large study of this which he reported on in his 1998 EPRI report. It was called the 'Degree of Loading' experiments and consisted of about half of the reported effort (450+ page report). The use of a histogram to illustrate the results is perhaps not the best way for analysis, but is good for visual impact on the audience. In the end...need more data.
That 'more data' would need to probe various hypotheses about what is going on, not just be 'more of the same', i.e. a little tinkering on methodology would be indicated.
I also note that you've made a transition in your question that many haven't made yet. Associating CCS with that graphic requires connecting apparent excess heat to an ATER/CCS issue. Most refuse to even consider such.