Everyone wants to start at Happy Isles or Whitney Portal. Just start at either Horseshoe Meadows in the south or one of the TH near Tioga Pass in the north. Yeah, you miss the start, and the mobs, but you can pick up the trail where the crowds have fallen off and you still get the best of the JMT.
I've never done the whole trail, but I've hiked a lot of it, and it's spectacular country. It's been 15 years since I stood in Murdock Meadow in Evolution Valley, the memory still gives me goose bumps. No range like the Sierras. Wind Rivers comes close.