After an unbelievable amount of burned time untangling and rebuilding cartridges, I figured out the the cutting blade mechanism was out-of-sync with the electronics. Maybe it had jumped a tooth at some point. By unplugging power and removing the battery then restoring the battery, I was able to provoke it to re-home on power-up. The blade and the black clamp foot moved back and tape could again flow freely!
In the mobile app (but not on the desktop version), there is a function to reveal the blade for cleaning purposes. My big break came when I noticed that the commands seemed to have the opposite effect to their labels on the UI.