Posterior predictive p-values---how to present multiple comparisons and how to deal with 0?

How do you summarize posterior predictive p-values analyses of a hierarchical model when the summary statistic you want to test is at the lowest level and there are ~10000 groups? I was thinking I would just make a histogram of all the p-values. Would you find that acceptable? For clarity, I’m trying to do something along the lines of chapter 6.3 here

Somewhat related, how do you deal with posterior distributions that have most of their density at 0? If, say, the posterior predictive distribution has 99% of its density at 0 and y=0, the {p_B} = {\rm{Pr}}(T({y^{{\rm{rep}}}},\theta ) \ge T(y,\theta )|y)=0.01 and the flipped tail-comparison {p_B} = {\rm{Pr}}(T({y^{{\rm{rep}}}},\theta ) \le T(y,\theta )|y)=0. That is, the p-values look horrible even though the model prediction is good. Is it acceptable to count half the density at 0 as \le and half as \ge, giving instead p-values \approx 0.5?