Here's a link to the ink cartridges that we buy from Amazon. We've never had an issue with them before.
The tape is removed, and the nozzle check looks totally fine, no problem at all. That's the part that is really throwing us for a loop.
In the interim, the stopgap solution I stumbled upon is changing the media type of the print job to photo. For whatever, reason that works - albeit with extra steps and slower printing time.
It's not a graceful solution, but it's getting the job done, in a pinch.