I think the drop rate is fine. I spent almost a combined total of 25 hours in Central Shroud before I got mine, and only needed to do 3 FATEs in Western La Noscea for the next one; that's RNG for you. I think the best way to go about the farm is to not think that you'll get any ATMAs at all while you're doing the FATEs, and just go into autopilot as you move from FATE to FATE (listening to music helps with this). It's a long-term project, and you can't expect to get them all in one or two sessions.

What WOULD be nice is if you had to have a Zenith to get the quest (like it is now), but let you farm the FATEs with any class/weapon combination. I really don't see the reason to have your Zenith equipped for the farm.