I did the JMT a few years ago and when I was planning it, I couldn't get any permits southbound out of happy isles or northbound from whitney portal but if you just started south of whitney at cottonwood pass it was a lot easier to get permits. In fact, if you went before a certain weekend in june there was literally no quota so you didn't have to do a lottery at all. And once you secure your starting permit, you can go as long and wherever you want. The permits are mostly to manage parking and crowding at the trailhead, so if you want to hike all the way to yosemite you can (as long as you say so in your itinerary).

That section from cottonwood lakes to Whitney summit to Kearsarge pass was super cool and would be a good big vert, high elevation 4-5 day hike if you didn't want to do the whole JMT.

if you are interested more in that BM me.