Hi John,
In 2003 I did this very segment. I resupplied at the MTR and 4 days and 80 miles later hiked out at Onion Valley. There is not much practical opportunity to resupply along this stretch of the JMT. It seems that careful planning is paramount. Despite catching numerous trout, I still hiked out over Kearsarge Pass with no food left. I then used the standard Garcia bear canister and devoured its contents rapidly, as I eat (when possible) large meals in the backcountry.
Last year (while doing the combined HST and JMT) I resupplied at the MTR, left the JMT at the Le Conte Ranger Station and hiked out over Bishop Pass. Later in the week (after a resupply) I returned to the JMT over Bishop Pass, resumed hiking south, and then again left the JMT over Kearsarge Pass.
What an awesome area of the JMT! Have fun.
Jim F