Yea, I saw references to the 7/8-20, but like Steve said, that wasn't the right fitting for my carburetor and seems like it would be much too big.
Here's a photo of my old fitting on the right and the new fittings I purchased on the left. Both of those parts on the left were separate parts, both in sealed Russell bags, and both say 9/16. And they do fit together nicely, so I think I have what the labels say.
I measured the outside diameter of the old fitting threads; they are 0.663" (between 5/8" and 11/16") and they do seem to be tapered.
The OD of 3/8" NPT pipe threads is 0.675, that's why I mentioned that in the original post. Counting the threads per inch, this fitting has about 9 in the 1/2" that's there, so 18 per inch, which does match the 3/8" NPT. But again, that's just a good guess.
I just put an email into Holley. And I've been rummaging around the Summit website, but no luck yet in finding a banjo fitting. This should be easy!