ADC reading occasional non-zero with pull-down

The Pro-mini should return zero with it's analogue input shorted to ground.
Are you also using other analogue inputs?

Using 1.1volt Aref is no different, resolution wise, to what you're doing now. But readout should be more stable.
Resolution is still 1024 A/D steps, minus the small amount you loose from the 'wrong' ratio of the divider.
I don't see why you can't have a 0.1volt display with a bit of oversampling (multiple A/D readings and averaging).
Input voltage can still be 0-VCC with 1.1volt Aref enabled.
The A/D will just return 1023 when you input more than the Aref voltage.
The advantage of using 1.1volt Aref is that you can now input ~400volt into the divider before you reach 5volt on the tap.
Leo..