Another option is to daisy-chain 8 of these: MAX11131AUI+. They are 12-bit 16-channel A/D converters that can run up to 3MSPS. Mouser has 12 in stock, and they come in SSOP-28–difficult to hand-solder, but manageable.
Alternatively, you could daisy-chain 16 eight-channel A/Ds with a more friendly package: MCP3208-CI/P is a 8-channel, 12-bit A/D in a 16-pin DIP package. Yup, the 0.1" pin spacing that you can breadboard! (You have to love Microchip for thinking of the hobbyists! On top of that, Mouser has 423 in stock.) 100ksps should be fast enough for air pressure, I assume. (If that isn’t fast enough, you need a microphone )
Both of the above A/Ds support SPI. While I haven’t daisy-chained SPI devices before, I don’t see any reason why it won’t work. (It could be a little challenging to sort out in software, though: be forewarned!) I2C would be easier to handle (set each device to a different A-code), but you can only have a maximum of 8 same-type devices on a bus, and I couldn’t find any 16-channel I2C A/D converters.