I too would go with tdtz's recommendation -- make your trip reservations, and make all the plans. Only thing I might add if at all possible, is give yourselves one extra day of wiggle room -- plan on hiking either Monday or Tuesday. If you come down on a very short trip, you run the risk of having serious altitude issues anyway. If you didn't get your permits on Sunday for the Monday hike, come back again on Monday for a Tuesday hike.

And spend a day acclimating and enjoying the high altitude of Horseshoe Meadows or a similar spot in the Sierra.

If you cannot add the extra day, just have a Plan B. You could drive up to White Mountain and hike that, or you could day hike Mt Langley. Both are memorable and enjoyable Fourteeners.

But I am pretty sure you would be able to get the permits you want.