Alternate perspective here:
My favorite part of the JMT is the section between Evolution Valley and the Bullfrog Lake/Kearsarge Pass area. (In other words, the entirety of Kings Canyon National Park.) I do not think the section from Kearsarge to Whitney is quite as drop-dead gorgeous by comparison. The miles through the Tyndall Creek area are even a bit tedious.
Try to do Whitney, of course. But if you have to cut it short at Kearsarge - a very pretty and well-graded pass to exit, by the way - IMO you will still have seen the best of the JMT. On your exit, try to camp at Kearsarge Lakes (rather than Charlotte Lake), and take the more southern trail to Kearsarge Lakes that passes through Bullfrog Lake. Outstanding views and gorgeous camping.
If you miss Whitney, it's easy enough to come back. A jaunt through Sequoia NP (along the High Sierra Trail, or maybe from Mineral King or Roads End), ending at Whitney, could make a very nice week-long trip in the future.