Your explanation doesn't include any "DC shifting".
Do you know the resolution of your ADC? If its full range is 5V for 255 values, then each increment would be about 0.02 Volts. So 2.6V would be about 133 and 3.2 would be about 163. How is that not enough resolution? It's more than ten percent of the full-scale range, if your ADC does 5 Volts. And regardless of the voltage range of your ADC, "15 or 20" counts difference would be about 6 to 8 percent of the 255-count range. Is your noise so large that you can't see a 15 or 20 count difference out of 255? Or what is the problem?