Which voltage regulator should I use?
IGND which is mentioned on page 4 of the datasheet is apparently proportional to the output current. This accounts for about 2-5% of the total current drawn by the regulator, depending on its load. With the maximum voltage drop of 4 - 3.6 = 400mV, a switching regulator will make no real difference. I think your only option is to find another regulator that has better efficiency.