I’ve had some success with P(Y > c) for a sensible c thad divides the ordinal response roughly in the middle for most cases.
Here is a custom plot I made and found useful, it combines some elements of PPCheck with exploring the implications of the model. For each data point I make predictions by varying a single variable across the range of its values:
The veritcal bars show posterior credible intervals. Each line connects all predictions from the same sample and the same data point (a random subset shown), green circles are the observed data (size indicates number of cases). Line blue when the probability increases and red when decreases.