Hi there,
You have made the right decision of applying to 6 B-Schools at a time. If you apply less, you may have lesser options/chances and if you apply more than 6 B-Schools it can be difficult to meet every B-Schools deadline at the same time.
You have categorized very well. MIT Sloan and Yale business school have acceptance rate between 13-19% approx. and can be targeted as stretch B-Schools as per your profile and GMAT Score.
Oxford and Cambridge B-Schools have 25-27% approx acceptance rate and are within your reach. You have fair chances of getting an admission. You can also add NUS to second category B-Schools list.
Manchester's acceptance rate is more than 40% so you have higher chances of getting admission to this B-School.
I would suggest you to work meticulously on your B-school essays and get it reviewed from your colleague, supervisor or professional consultants before submitting your application. It will make your profile strong.
You may also visit
https://bit.ly/XRH1Lw for essays and analysis.
Feel free to send PM if you need any further assistance. Hope that helps.
Cheers!