Another reason for dropping from 3 days to 2 is that in addition to saving the weight of food for another day, you also have the potential to substitute a self-service stay at Carter Notch Hut for the weight of the shelter you'd otherwise need to carry.
I also would favor south-to-north for the reasons TEO stated, but there is a serious caution. Depending on when you're going and what Mother Nature chooses to do, you could be looking at substantial ice down the north side of N. Carter. That stretch is steep, ledgy and difficult even at the height of summer. When cold (there has already been rain and freezing temps there), the ice warrants extreme caution. Unless you're armed with up-to-date intel to the contrary, traction and a rope (at minimum) would be a really good idea.
Because up is less hazardous than down, at the expense of 1000'+ of elevation gain you could mitigate some of the risk by going north to south. Were you to do this, you can avoid a steep descent off E via a cakewalk down Polecat from D. While also steep, ice down the south side of Carter Dome is more likely to be manageable early-season.
Last, a bit of math to consider in the event that your fundamental objective is to get the peaks, with backpacking being merely a means to that end rather than an objective in its own right. The full south-to-north hike from Glen Ellis to Bangor Street is 19 miles long, with just under 7000' of elevation gain. Dropping Moriah from the equation brings the numbers down to 14/5900. The latter constitutes a moderately challenging hike for someone in good shape with a day pack. Following that with a frugal stay in Gorham ($24 & up), you could then rest up and enjoy Moriah (10/3200) as a separate day hike. Your 2-day total is 5/2100 greater than if you did the south-to-north backpack, but you're doing it with a day pack, and you're avoiding North Carter altogether.
Alex