Per immigration department, the new contract can be submitted only 28 days prior date of expiry of existing contract. So you can only apply around mid August.
Why don't you call and check the time for application? If it takes, one week, you still can give her the 2 weeks annual leave by end of August to early September. Then it will save all your trouble.
Since your main concern is you must have the maid start working for you on September. Then, this leave you no choice but play with the rules. My sister has the same case and she told me that the contract submitted is for 2 years, but the visa issued will be 1 year if the maid does not leave HK immediately after the old contract. Remember that that there is a start of contract date/visa date. So,within 1 year, your maid must leave HK and re-entry. When she re-entry HK, a visa expiry date will be stamped on her passport. So, you only need to arrange her to Shenzhen for 1 day, even same day return and get the new extension of visa upto your new contract 2 years period.
Again, you should call the immigration department to clear all your questions.