jla, White Mountain is a walk in the park compared to Whitney, and a lot of mountains much lower in elevation IMO. It's only difficulty (from the dirt road) is the altitude.
I'm an average guy in average health, and found the hike to be relatively easy. The elevation gains are very gradual except the last mile.
I'm reading your post in two different ways:
1) You have three days to acclimate AND summit Whitney. Acclimate near White Mountain, summit White Mountain, summit Whitney. If this is the case, yes, I think White Mountain is too much.
2) You have three days to acclimate, and three more to summit Whitney. If this is the case, you'll be more than fine.
