Christopher, I'm not sure you actually disagree with these points, but I think they relate to the topic at hand, since they do indicate technological progress occurring in the films.
Very clearly, the Death Star represented a technological advancement. It was a weapon the galaxy had never seen before. We know so little about the details of its construction and engineering that a position dismissive of the kinds of innovations necessary to construct it is unsupportable. The fact is that it was depicted in-universe as being something new.
Upthread,
Caliburn24 pointed out innovations in fighter technology. One of the things that's evident is the evolution of hyperdrive technology as applied to fighters. The Jedi fighter of the PT needed an external hyperdrive ring. X-wing class and later had internal motors. That's an obvious improvement, because needing to park a hyperdrive ring is very bad from a tactical point of view. I find it the most plausible explanation in the PT that smaller hyperdrive motors simply weren't available at all. As valuable as the Jedi were, the Republic should have spared no expense whatsoever on their fighters. Therefore, the mere existence of hyperdrive rings proves that better hyperdrive motors were simply not available
at all.
Now you can also be dismissive of the modifications made to the
Falcon as something akin to the tinkerings of grease-monkeys, but when the whole OT is considered (actually, the PT too), IMO that too is not the most likely truth in-universe. It's true that Han's bragging came off as a sales pitch of questionable veracity. That was certainly true the first time with respect to the comment about the Kessel Run in the Cantina. Clearly, Obi-Wan didn't believe it. But why? Was it because Han used the wrong unit of measurement, or was it because nothing could go that fast? It's a question worth asking for two good reasons. The first is that, as something to counter Luke's impression that the
Falcon is a piece of junk, the point-five past light speed line is delivered in a way that seems completely believable. Whatever point-five past light speed means, it's supposed to be true that the
Falcon can go that fast, and it's supposed to sound impressive. Secondly, in TESB Lando asserted that the
Falcon was the "fastest hunk of junk in the galaxy". Again, there are two ways to read this line. Either it's fast, but only for a hunk of junk, or it really is fast compared to anything and it's something cobbled together from spare parts. In the context of something that saved his life quite a few times, the second alternative seems more likely. Finally, observe that the
Falcon was regularly able to stay ahead of the curve in battle against Imperial forces. That tells us that there really is something under her hood, and that in general underestimating her is a bad idea. All this paints a picture of a ship that has genuine cutting edge performance in the galaxy, and as such is evidence of there having been end-user innovations made at some point on the Outer Rim. Most likely the "fundamental" one [i.e. the most important one] applied to the
Falcon was made before Han won her.
Also, since the Republic had collapsed, it's completely realistic that cutting-edge innovations would not be imported into the Outer Rim anymore, as apparently they hadn't been for some time by the PT. Improvements to the quality of life in the Outer Rim could only be home-grown in the Outer Rim. This idea is supported by the presence of Jawas in the OT, the junk dealers in the PT, and even the Pod Races. It is further support of the idea that the
Falcon was cutting edge (ETA: by this I mean that it is consistent with the idea that the
Falcon outclassed ships all over galaxy, and partially explains it), as the "fundamental" innovation applied to make her so special, having originated in the Outer Rim itself, could easily not have been applied to anything else outside the Outer Rim. In particular, it could easily have been unknown both to the Empire and to the Rebellion, at least until Han joined it. Furthermore, this is completely consistent with the idea that hyperdrive motors were better on the X-wing than on any fighter available in the PT. Innovations on the Outer Rim to make the
Falcon might have been addressing the same need to improve the state of hyperdrive technology, as it existed at the climax of the Republic, but
independently from the inventors who developed the X-wing.
So, you're saying that the Rebels were actually hardly impressed, and they just attacked both stations largely for kicks? Part of the premise in the Death Star is that large enough quantitative charges are qualitative. 
