I would reserve on the entry date, and also the exit permit as far out as possible. You will have that in the bag.
If you have the entry permit and the (too early) exit permit, you might try changing the exit permit date online on progressively later dates, to see if the online system allows that.
Also understand this: The TC exit quota is 25 per day, but only 15 are reservable online. The other 10 are available for walk-in people and adjustments for people like you. With your exit date so far out, most of the 10 should still be available for you.
However, I would also call the Wilderness Permit Office number, 760-873-2483. Cindy or John may have better suggestions. You should call them now and explore your options. If you can't move your exit date farther ahead online, I think they could probably do it for you.
If all else fails, carrying that permit, I am pretty sure if you explained to the ranger on the trail what your predicament was, there wouldn't be a problem. They are most interested in the fact that you do have an exit permit, and understand that trips don't always take exactly the number of days initially planned.