If you prefer analog devices, they have their AD1937/AD1938/AD1939 which contain 4 ADCs and 8 DACs each.
There is no question if you use discrete separate stereo ADCs and DACs, your SNR on the ADC side will improve drastically.
But remember, you were thinking of feeding 16 analog audio signals through 16x16 analog switched/volume controls. Even with a separation of 90db between everything, all that cross-talk and board routing will have summed up with a total system THD+N only in the 85db range unless you only had 1 or 2 audio sources running.
The FPGA solution would also offer you a free digital 16 channel TOSSLINK / ADAT audio interface output. (hmm, you are approaching 100megabits/sec for uncompressed full 192k/24bit/16channels.)
If you want an Analog devices 8 channel sampler with studio grade performance, use this guy: AD7768
All you need are 2 of those ADCs and choose an 8 channel studio grade DAC for the other side.
Careful and do not order the -4 version, that one only has 4ADCs in it...