I live in Medway and my dd took both the Medway and Kent test, as her English is not as good as her Maths. She passed the Kent test with a very high score but missed the Medway by 5 marks. She was offered her first choice school on allocation day - MGGS. We live just under 6 miles from the school.
Your dd should definitely get into a Maidstone Grammar school if she passes, although you will be worried sick until you get the offer letter!
Your dd could sit the Medway test as well as a backup if you're worried about not been allocated a Grammar school.
Please note - if your dd attends a Kent school, she might not qualify for a free bus pass unless the Kent school is deemed her nearest appropriate school and as a Medway resident she doesn't qualify for a Kent freedom pass either.
Feel free to pm me