The right way to shop around is to request an official Good Faith Estimate from each lender you're interested in.
You haven't paid for an appraisal yet, have you? They don't transfer between lenders.
I doubt a bank would haggle on an interest rate. I shopped for a refinance by finding the lowest rate and closing costs, which I found at aimloan.com, which has a 2.625% 15 year loan (might be for 75% LTV). The only catch I know of is that underwriters for lower-rate lenders are typically more conservative. If you get turned down, you'll have to pay for another appraisal.
Are you sure you want a 15 year? They also have a 3.25% 30-year.