So, you did get the differential input about right, but not the role of Vref.
The ADC will convert the *differential input* in the -Vref / +Vref range. If you use a Vref of 3V, then your differential range is effectively +/-3V, which is not what you want.
With a Vin- at 2V and the expected input signal on Vin+ between 2V and 3V, your differential input is in the 0V / 1V range. You'll need a Vref of 1V to get the full positive scale for 3V input.
And yes, you'll still lose the negative half in this case, so 1 bit of resolution.
If you want to get the full ADC resolution, you'll have to approach it like this:
- Put a reference voltage of 2.5V at Vin- (instead of 2V).
- Use a 0.5V reference voltage for Vref. (Vref accepts from 0.1V to VDD, so no problem there.)
You'll get the full 22 bits, obviously "centered" around 2.5V, but that doesn't matter, you'll just use the numeric output appropriately. You'll have negative values for inputs in the 2V to 2.5V range, and positive from 2.5V to 3V.