Am Tilt Madness

[Warbuff]

I was at the final table of a free roll and 2nd in chips with roughly 1.2 million it was 5:45 am and had been up all night with about 90 minutes to go before I had to leave for work. I needed to get an hour nap in so I wouldn't kill myself driving in to work. Anyway, the chip leader had about 1.6 million and the rest of the stacks were 150k to roughly 500k, to make a long story short I pushed all in with A Q and was called by the chip leader with KJ flop came AJJ and I was busted. I had waited for a decent hand to go all in with since the chip leader had pushed in 11 times in a row and was just running away with the blinds. So I finished 7th however I think the better play would have been to put myself on auto fold and and get my much needed sleep since my stack was more then double that of the 3rd largest stack(500k) I probably could have auto folded myself to at least 3rd place finish the blinds were 10/20k and were raising every 10 mins. Any thoughts on this and the math behind such and idea would also be helpful