If you use the DSP filter approach you will be able to optimize your antialiasing filter for low offset. If you're filtering down to the sub Hz you can _way_ oversample, use a cheap slow processor, and still have an anti-aliasing filter with decent-sized caps. At this point you don't have to give a damn about the capacitor drift, you only have to worry about the DC offset.
As an added benefit you'll be filtering any ADC noise after it's been sampled, thus increasing the effective ADC resolution (but not accuracy).