I know they're available all around Mooshu, but is there a "best" place to find them? I've tried Jade Palace and Ancient Burial Grounds, to no avail.
It really imo depends on the luck. I'd try going for places that don't have many types of fish, so there's a bigger chance there is a origami, or places with lots of water so there are a few different options rather than just one big area. Hope that helps :)
Jade Palace and Shoshun Palace are among the easiest places to find them.
To find them, there are multiple ways depending on which spells you have. If you have Winnow Rank 2, use that and then cast Reveal Fish School. Origami Fish is the only Rank 2 Storm fish you'll find there, so if you see a Storm fish, that's the one you're looking for.
If you don't have Winnow Rank 2 but you have Winnow Storm, use that. If you have Reveal Fish Rank 1, you can use that too and look for any fish that don't light up.
If you don't have Winnow Storm, just cast Reveal Fish School. The Origami Fish swim very fast, so look for the quick fish in the pond. The only fish in the Jade Palace that swims faster than the Origami Fish is the Goldfin-ger, which is Fire. So when you find a very fast Storm fish, it's almost guaranteed to be an Origami Fish.