So yeah, Treefish are indeed caught at the Park in Willow Creek. I haven't found a Batfish outside Forgotten Grotto yet, however. I'm about to go to Sylvan Glade because it looks like the truly unique fish there that is hard to find or impossible to catch elsewhere must be the tilapia. Most fishing spots are the same, and those listed by Nutella are the actually interesting ones. This is rather unfortunate to me, as I wish there was more diversity to spawners. I basically am going to end up telling people to go to 5 places..
Edit: and I'm also going to tell them why these uncommon fish present more trouble than the rares. We have yet another bug affecting collections. I wondered why my level 10 fisherman couldn't find Catfish at, well, literally every fishing spot in my neighborhood all of a sudden. On a hunch, I cheated and dropped her skill level to 4, which is when you unlock Tilapia and Catfish. I caught a catfish, great! I immediately went to Sylvan Glade's waterfall spot and got my Tilapia, finishing the collection.
There's nothing changing game to game... at some point fishing bugs out and you're not able to catch catfish and tilapia. All other fish are catchable except those two, and every fish has a set location it can be found in.