Sorry if this is too obvious, but don't forget that 13,000 feet is way above treeline and the lightning danger can be extreme. Best to plan on *possibly* sleeping that high, but only if weather looks exceptionally clear. And choose your sleeping site carefully !
Also, if you jump right up to 13000 ft, you may find that adaptation is unpleasant and you are unable to sleep. But its pretty unpredictable.
Anyway, I've been doing something similar, hiking and sleeping as high as possible (11-12,500) for 3 nights at a time. Hard to disentangle the results from improvements in fitness, but I definitely feel much more comfortable at 13-14,000 feet.
"They" say that your body is at its worst in the 2-5 day period after arriving at altitude. Who knows how precise the timing is, though.