I've been told by Inyo N.F. staff that with the switch to a new reservation system last October, now this year people like you should be able to reserve both entry and exit permits on the 6-months-before entry date.
And that may be why you are seeing all the TC exit permits totally reserved already -- by people like you getting their entry permit, and also reserving the TC exit farther out than 6 months.
You should give it a try before Feb 25 and see how far you can get with the Entry + Exit pair of permits. You can always cancel the reservation before paying.
Good luck! ...and please report back how it works out.