Ohhhh ADCs, it's always annoying looking through all the specs to find the perfect one.
I've spent quite a bit of time digging through websites to find an ADC that's not bad. Something that's good at what it does but not over-the-top. What I've come up with is the THS12082, a 12bit dual-channel 8MSPS ADC with a FIFO and a parallel interface. For a TSOP part it's almost $19, so it's not exactly cheap, but I think aside from the BBB the total part cost won't be outrageous. Not that the BBB's price is outrageous, but you know what I mean.
This ADC seems quite good. It will be able to sample both the I and Q signals at a very reasonable rate with a good amount of precision. The FIFO relaxes the requirements for needing a perfect PRU implementation (however I'm not too worried about that). The parallel interface eases signal integrity issues going through the BBB headers. So yeah, I think it will do an admirable job.
Now I just have to worry about the op-amps and the amplifier circuit.