Short of more substantive changes to the Fate system, the changes I'd suggest are as follows.
Increase the Atma drop rate slightly. Right now there's a 1-2% chance of an Atma dropping on any given fate. I'd change that to 4% for most fates, 2% for item delivery Fates, and 6% for Boss Fates. This wouldn't make the process dramatically faster, but it'd dramatically reduce the chances of you going an hour without getting an Atma drop.
Reduce the number of Myth Tomes needed for the books. You need nine books at 1.5K Myth Tomes a pieces?! You'll need to do a fair amount of Grinding just to get them. I'd say, lower them to somewhere like, 1000-1200 Tomes.
Can't really comment on the Book Grind, if it's predictable I don't see it being a huge problem.
Increase the amount of Gil that drops on Fates. Often you're only barely making more money then you're putting into repairs. If you could accumulate a fair amount of Gil after a few hours, it wouldn't be as big a deal. It'd have to be fairly subtle of course, or else it'd send the game economy outta whack, so to speak.