Unfortunately you will still have to pay the extra stamp duty and claim it back. You have 30 days to pay the stamp duty but it is calculated on the dates of sale and purchase. Any way you could shift your purchase date to sync them up?
The firm I work for completes the SDLT paperwork at completion so monies need to be in their client account at this time. As you will technically own two residential properties at the end of the transaction you do have to pay the higher rate but when your first residential property is sold, you will be eligible to claim the extra stamp duty back.