Sorry to be kind of joy-killer, but I am sure, that a 31-bit conversion is meaningless. The accuracy of EVERYTHING would be beyond anything possible today with standard components and technologies. Or that you may get 31 bits, where at least half, and maybe more of bits are just plain noise and have no usability whatsoever. Thermal noise alone is going to sabotage your ambition, let alone practical component accuracy and stability.
Even with slightly less ambitious plans you should also differentiate between supply voltage accuracy and reference voltage accuracy. The reference volatile should be stable and accurate and with low noise. Of course, if you only want relative readings, you may use less accurate reference than your targeted conversion accuracy is, as then things compensate automatically.
On that background generating negative voltage is likely one of the smallest headaches. Suggestions above can be completely OK - and there are more possible solutions - so long you don't attempt accuracies in magnitude of billionth of a volt..... For that, there is likely no practical way, and even any theoretical way is hard to find!