I've used fast SAR ADCs in the past, but they are typically not low power, and require driving. The one that you are suggesting, for example needs a fast opamp, driving a 16pF capacitor into less than 1 LSB settling time in less than 1 uS.
The ADS7054 spec is approx 900uW at 1.8V which is better than many (but not all) delta-sigma convertors for a given data rate and resolution. You don't need fast driver opamps to measure low frequency signals - use a large capacitor to provide the sampling capacitor's charge - 16uF should charge the 16pF to within 1ppm providing the ESR is low enough.
You would need extra circuitry and power consumption to provide the dither signal if the INL isn't good enough.
And while the oversampling sounds like a possible way of doing it, I would need to characterise the entire system, including the sampling.
Yes there could potentially be a significant amount of work to characterize the linearity depending on how low it needs to be. I would however hope that you'd do some testing whatever ADC you used rather than relying on the datasheet values which are frequently wrong (or at least optimistic) or only valid for unrealistic operating conditons.
And beat or software developers with a stick for days, until they get the algorithm right.
Oversampling is just averaging the input samples - adding some numbers together and dividing the result shouldn't be too taxing for even the most deadbeat developers. Getting them to generate a dither signal with a DAC and sycnhronising the sampling/averaging to it would be a bit more effort but hardly challenging compared to the effort required to properly comprehend, configure and use many modern ADCs with comprehensive configurability including PGA gains, filter types, input buffer settings, clock settings, modulator divider ratios, calibration settings etc. Take a look at the AD7768 for an extreme case.
The ADS7054 looks particularly good in this respect with no configuration required apart from the offset calibration.
Given your 1.8V requirement, have you found many other options apart from using a dc-dc convertor to provide a higher supply voltage? Have you found any suitable ADCs?