It sounds like early to mid april may be best for you, and you could likely finish by mid to late September.
If you want to go with most of the “pack” any time in April should be good. There will probably be a LOT of people starting then. Leaving in May or early March means less people. People who move fast can leave pretty late. See the journal of Ken and Marcia from 2003 for an example of relatively fast, late start hikers. They had already completed 2 long distance hikes though, so keep that in mind.
My husband and I started March 4th 2002. We had some cold days (8 degrees F. was the coldest) but absolutely no snow. I guess it was a mild year. Plenty of other hikers started in March for us to socialize with, and we had 90 degree weather our last week in Maine, (mid August) which meant awesome swimming opportunities. However, because we left when we did, a few hostels were not yet open for the season when we got to them. And of course we missed the beautiful New England fall colors by finishing early. It took us about 5 1/2 months and we never felt rushed or too slow, but everyone is different. Bottom line is, you can have an awesome time no matter when you start. Read some trailjournals for some weather experiences, and call or email some hostels (Miss Janets, Blueberry Patch, the Hike Inn come to mind). The hostel owners are full of stories and advise about the weather, as they are the ones who’ve been the “shelters from the storms” in years past.
Jitterbug