(1) Apply in Round 1 this upcoming year.
(2) Retake the GMAT.
These were the two things that really hurt you (applying late, with a mediocre GMAT for your target schools). If you want to target a top 16 school, you need around a 680 or higher (and ideally above 700) to be safe.
On the surface, it seems like you have an interesting enough story to tell, so I'd give Stanford and Berkeley another shot. Stanford is a stretch for just about everyone, but assuming you apply early with a higher GMAT, then it's at least worth giving it a shot.
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