Well, I have kind of the same problem.
I've made a 21-bit ADC. However the output rate is 25Hz. So, it takes ages to measure DNL especially if you want to hit each code several times for a histogram.
For the case of INL, you don't need to hit every code. Just take a number of samples over the full range, and you'll immediately see the deviation from an ideal transfer characteristic. But, be aware that there's no such 22-bit linear signal generator. So, you need to measure your input signal with a high linearity ADC or digital multimeter. I use Keithley 2002 to measure my DAC's output. With enough averaging, it has less than 1-ppm linearity. So, you can take the difference between your ADC's output and input and get the INL data.
For DNL, I'm still not sure how to measure it considering the time needed. Drift wouldn't effect the differences between each code I guess, but it would be meaningless to integrate that DNL data to get INL from DNL. So, that's a really tough problem.
BTW: I'm now working on a 20-bit ADC for audio bandwidth. Is there anyone who has any idea how to generate high linearity sine wave for such resoultion? SNR is not a big deal as far as I see but the most critical spec of the ADC would be THD, o I want a really pure sine. I think I need to just specify some frequencies and make a very narrow bandpass filters. But it would be really hard to make it in very low frequencies I guess. I've found NI PCI-4461 card which has perfect analog input charachteristics but it's DACs lacks of the THD performance I need.