A relative lack at the species level, yes.
Both of those statements are false. PE has been hotly debated within the scientific community, and it has been debated on the basis of observed data. The jury is still out about how accurate it is as a broad description of morphological change, although there is agreement that rates of change vary a lot.
As for testing. . . have you ever actually read the Gould and Eldredge papers, or any of the other scientific literature on the subject? Here's one of the figures from one of their papers, showing a disputed data set:
It shows size as a function of time for a single species; note that each point represents many individual fossil organisms. The dispute between PE and phyletic gradualism boils down to deciding whether that plot represents continuous change or stasis interrupted by short periods of rapid change.
Here's another figure from the same paper, showing a lineage of 5 early mammals.
Again, does this represent gradual change, or is there a punctuation event or events in there? These are all very similar animals -- you'd probably call them the same animal if you saw them.
Note that the number next to each bar in the second figure represents the number of specimens in that sample. That's something like a hundred transitional fossils in this one tiny part of the tree of life. Is this too few? What is the creationist explanation for these samples, and the overall pattern?
ETA: My figures aren't showing up for some reason. Here are links to them:
First.
Second.