I have hiked Half Dome at night at least 15 times over the years. I honestly wouldn't recommend this unless you know the trail well enough in the daytime. There are several sections where you might go astray or just not know where to go.
Since you're avoiding the Mist Trail and doing the JMT route, after you reach the area before the bridge, you will almost certainly have no idea where you're going in the dark. There are no signs and you might just be stuck or wandering around aimlessly, wondering, "where do I go?" If you know the trail, it's not an issue. But I would never hike Half Dome in the dark without knowing from daytime experience.
In addition, once you get to Little Yosemite Valley and the sand portion, you can't get lost there, but many people erroneously believe you're almost done at that point. When they reach the sign at the end of LYV and see you have 4.5 more miles to go, I've seen countless people turn around.
If you do it, make sure your have extra batteries for your headlamps and bring a flashlight as well. Because if something goes wrong and your bulbs go out, a flashlight will enable you to make progress in the dark.
Finally (and I realize I'm sounding like a party pooper and I do apologize for that),
.... the view of the sunrise at the top of Half Dome is really not that spectacular. The view from the top of Clouds Rest is by far the superior view, IMHO.
On the plus side, starting Half Dome at 2:00 or 3:00 is fantastic because there are no people on the trail. You'll have it all to yourselves. Be prepared also to tack on another .6 miles of walking if you're starting from Curry Village cabins.