I had a few thought on the noise. The op-amp U10 is only relevant for the time the reference is connected. U9 (the intgrator) is also mainly important when the reference is active. Both OP-amps work togehter with the reference signal that does to the input of U10. So one kind of get a combination of the noise of the 2 OP-amps and the LTZ1000 reference. In this set the reference is usually the larger noise source by quite a bit.
Another point is that the time the 3 are connected depends on the input signal / voltage. With the variable time this gives a noise that gets higher the higher the voltage, not just from the principle low frequency reference noise, but also from higher frequencies ( > 99 Hz). The crude picture gives an added noise part proportional to the square root of the voltage.
With the relatively slow 20 s integration the extpected contribution is small - more like hard to see. If really an issue the point would be more adding a little filtering to the reference. The expected noise constribution is still small and though simple it is likely not really worth it.
The 2 main expected noise sources are jitter from the PLL - so the modification with the VCO range may help somewhat, though probably not much as there are also internal limitations.
The other point could be quantization, depending on what filtering is used in the custom prema chip. For the 2 V range the input amplifier can also contribute quite a bit, though it is still not that bad.
I have not seen detailed noise data on the 6048, but from the few curves shown at the start of the thread the noise is not that bad and with a 10 V test signal not that much higher than the 2 references involved.