NOT my tips, but those from refinancing experts who do this for a living:
1. You will receive a month off your mortgage payment as well which some people will take into consideration when calculating the break even point. In your case this would cover all of your closing costs...you just lose a month of principal reduction (which is going to be almost nothing anyway on a new mortgage).
2. You will also need to pay 9 months of taxes and insurance into your escrow account for a June closing, however, you will receive a refund from your current lender for the full balance of your current escrow account. Because this forces you into a higher loan balance you may want to consider an immediate principal reduction with the refund you receive from your current lender.
3. I'm not sure if you are paying mortgage insurance or what your loan-to-value ratio is but if you're up there you may want to have your lender consider a Lender Paid Mortgage Insurance (LMPI) product for you. This will result in a higher interest rate but the payment will likely be lower than a standard 30 fixed with MI.
4. If you sell within 10 years chances are that you won't have enough equity before that time to get out of MI anyway - assuming you don't have much equity in the property at this time.
5. You could also consider a combo loan to avoid MI and escrows if this is a concern for you and it typically results in a lower overall monthly payment.