How to present ping data from ICMP timestamp
You ask:


  How to make scientific sense of this data, for it to be easily presentable, and not blatantly wrong?


Well, the bottom line is: this data is blatantly wrong.  If your measurement method says that the latency on some link is negative 113 ms, there is something wrong with your measurement method.

Right now, you've got a "garbage in, garbage out" situation.  The data you've got does not survive simple cross-checks, which tells you that your measurement methods has problems.  What you need to do at this point is go back to the drawing board and devise a better measurement method.  For instance, maybe you can find some way to measure the offset between your clock and the remote machine's clock more precisely, and then adjust for that offset.

But in any case, it's pretty clear that the current measurement method isn't adequate on its own.