1)Your 1st priority is a smooth transaction. Close it first.
2)It's hard to float down the rate with the same lender. Some lenders don't even allow floating down. Even if the others allow, it's not free, usually, you will get 0.125% when the market is down 0.25% to 0.375%.
3)15 yr fixed rate is not down that much recently. In another word, the rates are almost of the same for most loan programs.
4)With QEIII, you might be able to refi lower rate later