After getting the keyboard reading all sorted out, the TI-57 firmware isn’t being bombarded with false keypress data all the time. Imagine my surprise when, after sitting idle for a few minutes, I looked at the LED display and observed  a “marching decimal point” moving left-to-right across the display. It can only be the original TI-57 built-in power save mode. My own power save mode, a winking decimal at the leftmost digit, kicked in a few minutes later. 

Now I need to measure current during each one to see which is better - I suspect it’s mine, because the TLC5929 is in sleep mode and the MCU is in idle mode the vast majority of the time. But the marching decimal points sure are fun!