I don't see how any of those things prevent the methodology I described being applied.
> If the suspect is a better match than N(1-p) of the other fingerprints, then the match has a p-value of p.
There may be no way to objectively determine if the suspect's prints are a better match than others.
More generally, I lack your expertise but it seems to me that statistics require data; we may not have reliable data. More colloquially, garbage in, garbage out.
Anyway, I recommend the National Academy of Sciences report, which is authored in part by their Committee on Applied and Theoretical Statistics.