I'm assuming your design passed timing, cause otherwise it would be simply kicking up the violated paths.
Also, there might be a simple cmd in certain tools to report this. But I don't know it.
That said:
Although you said you don't want the smallest-slack ones, I believe the one you are trying to find should be very probably buried in the smallest-slack ones.
Then if I were you, I would try setting a worst/smallest slack threshold and pick up those paths below the threshold, and figure out the combo logic levels. This could all be done with tcl/perl scripts.
Routing delay is also a contributor, but I would ignore it as it is usually not that influential given floorplan is reasonable.