Thanks to Kenny, I was well-educated as to what Mint Ponyland would carry. I'm only paraphrasing a bit when he said it was the best card store in Nagoya for singles. I got there about 45 minutes before closing.
I didn't spend much time going through the sorted boxes, but there were dozens of 5000-count boxes full of singles for set building in multiple sports, including idol cards. Singles start at 50 yen, which is more than the CAPS Mint location, but both stores would be good sources for people looking for specific singles when filling want lists. Being so well-organized, when I can return I hope to find some good oddballs and box set singles for my collection.
Mint Ponyland is located at Nakamurakoen Station from the Higashiyama (yellow) subway line. Use exit 6, and look for the Ponyland sign across the main street on an upper floor. It's very convenient to reach! If you're using a Mint point card, you won't be able to use it here, because they have their own.