The Lattice ICE40LP1K and ICE40HX1K FPGAs are big enough to support a J1a CPU (with 8K of RAM?) and are 1.4 × 1.5 × 0.45 mm and cost US$3.43.
The TI ADS7040 8-bit 1Msps ADC has an 8-X2QFN version that is 1.4 × 1.4 × 0.4 mm and costs US$1.14. It claims “nanowatt power consumption” by which they mean that it uses less than a microwatt at 1ksps. At 100ksps it uses 56μW, and the datasheet claims a physically impossible 49dB SNR (48.16 being the theoretical limit of what 8 bits can deliver). It uses 12MHz SPI and uses differential input. If you were to run it at 1Msps and downsample to audio 48ksps, you would gain about 7dB more.