The parking pull-off is 2.6 miles down (east) Passaconaway Rd from the Covered Bridge turn off on the Kanc. Look for the Forest service sign and knee high stones guarding the trail.

Note how we climbers screwed up the name. It is Eagle on the map, with Woodchuck further west.

I was about to say that your map was wrong... but turns out Google Earth's "Geographic Features" layer isn't accurate. It lists South Moat Mountain as 'Birch Hill'.

Here's another view of that approach:
www.invisiware.com/u/Image_10-22-2012_10.07.32_PM.png