The section that I suggested, from Leesburg to Purcellville and back, is mostly shaded (though the power companies are trying to get ahold of the right-of-ways and do the same as they've done east of Leesburg). There's one stretch in particular where the trees lining the trail make it feel as if you're riding through a cathedral.
It'd be great if you joined us, Janice! If you want to swing by my place, we could carpool up to meet Zen, then head across to Va and meet F8th.