I could see them going for a new sound a bit in Royal Scam, which was the weakest of the original five by a significant margin, but I did detect a hint of change on that album.
Katy Lied is split between the first five songs, which are all great, and the last five, which aren't so great. The last two are okay, but "Chain Lightning," "Your Gold Teeth" and Jon Walter's favorite "Everyone's Gone To The Movies" with the lame pedophile lyrics (CANCELLED!!!!) are pretty weak IMO. "Chain Lightning" is supposed to be about a fascist rally or something IIRC.
The two hits on Gaucho ("Hey Nineteen" and "Babylon Sisters") are still great, but totally overshadow the rest of it which got way too much into elevator muzak for me. Someone here really vehemently disagreed with me (Ben Greenstein?) but I've gone back to the album a few times and it never changed.
Their Grammy win has got to be the second or third most infamous, after Jethro Tull beating Metallica and Alanis Morissette sweeping in the mid 90s. I mentioned it to my mom at the time and she went "Steely Dan?"
That "Second Arrangement" thing is coming back to me now. I DID read about that at the time, but I've completely forgotten it until you brought it up!
There was also a guitar part in "Aja" that they supposedly couldn't recreate live (though they weren't performing live in 1977.)