Those i found (ti, cirrus) are designed for audio transmission (low THD etc), the problem seems to be the total gain error (1..2% of fs) which doesn't matter in audio applications.
You might find something around 10 bits of absolute accuracy, but it is hard to get much better than that. The reference that is used presents a limitation to the scale factor accuracy. To get better it would have to be trimmed and temperature compensated. I don't have exact numbers, but I can assure you that you won't find ADCs or DACs that will give you 14 bits of absolute accuracy.
That said, there are a number of parts from TI and ADI that are designed for instrumentation with sample rates up to the MHz range. Some are sigma-delta converters which may not be DC accurate, I'm not sure. But I know there are a number of them that sample in the 100's of kHz range up to about 1 MHz that are successive approximation converters with 16 or even 18 bits of resolution. These will likely be about as good as you can find. A year to two back these parts were being heavily promoted since they were new parts then (or at least had new variants). I can't say how easy to use you will find their interfaces.
Also verify the low frequency response, some chips intended for audio applications might have a low frequency limit in the 1-3 Hz range, so not useful if DC response is required. However, if you can perform analog voltage switching between a known reference voltage (ground) and the actual signal, this would solve this problem. With two or more reference levels, some linearity errors could be compensated at an expense of higher sampling frequency.
As for interfacing to the fiber, you would have to combine the clock and data e.g. using Manchester coding and at the reception site a separation of clock and data would be required, such as in the SPDIF system.
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