I personally view evolution as a combination of phyletic gradualism and puntuated equilibrium. The periods of stasis mentioned by OP could very well be periods in which PG is the dominant form of change. Though major events such as the permian extinction would open large niches in the so called "food chain" and allow for certain mutations to be more readily useful in adaptation than previous times, enabling PE.
It is important to note however, that the observation of a single species does not, and in fact cannot, be used as "proof" of a theory. There was a paper posted here a while ago, I'm not sure when, that compared the evolution of gars (lepisosteiformes) and polypteriformes, I'm not sure what the actual content of the paper covered but I have it on my laptop, I'll be able to look it over later and if it turn out there's interest in it I may be able to post it later tonight.
In any case the small amount of change in polys is surely indicative of their ability to adapt to their surroundings, and a testament to their ability to compete with other species. It's an interesting point you raised and I'm looking forward to reading more of this discussion.