$2700 rent on $2400 obligations only leaves you $300/month to cover vacancy, repairs, administrative expenses, etc. One month vacancy and you're in the red for nine months. Does not sound like a good plan to me.
You are looking at decreasing your savings by at least a third for the next 13 years (while you would be paying off the current mortgage) and even more for the 17 years after that (assuming you are looking at a 30 year mortgage for the new house). Is the new house really worth that?
How old are your kids? How much of a difference will it make to them to change schools? Do you really need more square footage? If so, are there any cheaper SF houses in the better school district or is this house for some reason a special bargain?
If this house you're thinking of bidding on were not on the market, would you be thinking about selling and moving? If not, I'd definitely stay put.