Right now the prototype suffers from two distinct problems. One is that there's some crosstalk of the LED rastering on the audio. That I believe I can solve by simply routing the audio line so that it doesn't cross under any of the raster lines. The other is the audio amp power issue I alluded to in the last log.
I've put in two designs for the next round of fabrication, and selecting between the two will be likely the last design change before a board-only product is ready.
One choice is to power the audio amp directly from the battery, leaving the boost converter to solely power the logic system. This is a bit dissatisfying to me, as the idea is that the whole system should get constant, steady power until it the batteries are "exhausted" and then it should just stop. A steady decrease in the battery voltage is going to mean that the audio will degenerate slowly over the battery lifetime. That said, in testing (albeit with fresh batteries), this resulted in completely glitch-free software. This is v1.2.4 in the Files section.
The other choice is switching to a beefier boost converter. The next candidate is the TPS613221A, which can supposedly make upwards of 500 mA (at a battery voltage of 2.5v), if I'm interpreting their charts correctly. In addition, the datasheet suggests that for high current applications, you place a Schottky diode in parallel with the controller, at which point the controller's sole job is to switch the inductor into and out of its charging configuration. This is v1.3 in the Files section.
We'll have an answer in two weeks.
EDIT: Another possible way to go is to use the TPS613222A boost converter to make 5 volts for both the audio amp and the LEDs and use a 3.3v LDO to power just the controller and flash ROM. This is essentially the same power configuration as the GPS talking clock, so I have increased confidence that it would work. The problem is that it's going to likely dramatically increase battery consumption with little real benefit. This would also require some minor software tweaks, as we would have to use an open-drain for switching the LED anodes off and on - the "off" voltage would be 5 volts, which the controller can't supply (a pull-up would be used instead). This just means switching the data direction lines instead of the output lines (with the outputs pre-set to 0).