The main board is going to host a number of components. First there's the power. The input voltage is some 17V AC. After rectification and smoothing, probably more like 14-15V DC. A 5V LDO will give me the 5V rail I need. I can then use a 3.3V regulator from the 5V rail to provide power to the 3.3V components (ESP32, SD card, etc.). This will power the main MCU - an ESP32 from Espressif. It's a powerful controller and should be able to handle the workload easily. It'll read from an SD card, output to an I2S DAC, get it's control from an NFC card reader and need to handle the buttons - at least in some way. It will also need to shutdown the amplifier when it's not needed.
The SD card interface will be simple - SD cards support SPI which can connect directly to the ESP32. The ESP32 also supports I2S. Interestingly, the ESP32 has a built-in DAC, but I would like to use an external one. I'm going to use a DAC module commonly found on eBay, AliExpress and Amazon based on the PCM5102 DAC from TI. For volume control, I will use a DS1801+ logarithmic digital potentiometer.
Finally, there's the amplifier. I've done quite a lot of research and have come to the conclusion that I'll build a Class-D amplifier for this project. The thermal envelope is small, power requirements are lower and it will run from a single power rail (this is all I have from the transformer). The TPA3122D2 is a through-hole, passively cooled Class-D amplifier that has few external components. At 15W, it's lower rated than the old Class-B 30W chip amp, but it shouldn't matter for this particular project. The TPA3122D2 is also a capable amplifier, so I'm not expecting any issues. The two speakers in the unit - a woofer and a "twiddler" (mid and tweeter combined) both present a load of approximately 6-7Ohms which are easily within the load for this amplifier.
The current main board by Bose, with the power connector removed (more on that later)
Finally, it's dawned on me that the main board is going to be a challenge to replace. The unit itself is wedge-shaped, which is somewhat of a challenge by itself, but there's also the battery compartment which takes a chunk out and the cutout for the transformer. Finally, the mounting screws need to be in exactly the right place. If that isn't enough, the whole front of the unit only has about 12mm of clearance between the PCB surface and the bottom of the speaker chamber. This is going to be fun!