Hey there,
Thanks for posting and congratulations on being such a great performer! You've got some awesome questions so let's see what we've got here.
1) Have none of your teams from those 4 - 8 week engagements been on other projects? Or have you literally worked with different teams for every project? If the latter, that's not ideal. But if you can find people at the firm who know you in a longer capacity or can speak to your performance over a greater period of time, that would be ideal!
2) I'm not sure what you mean by "strategy" but yes, that praise / performance should absolutely be included. I mean, that's one of the main purposes behind a recommendation letter. It's there to help you communicate, via a third party, how you compare to others. If by strategy you meant in terms of how recommendations are written properly or showcased, then yes, there's definitely a strategy but not one I can summarize in a forum post if that makes sense.
3) You're right that most are positive anyway but yes, it'll set you apart. I mean, if you have well established professionals at an MBB that can say these amazing things about you AND back them up with facts (e.g. year end evaluations, etc.) as well as examples, then that will automatically help set you apart. And they'll also want to show trajectory, consistency, and development.
4) The only real place to do that is on the application itself where they ask for awards / recognitions. Doing it anywhere else will make you seem immodest. You don't want to be too humble but there aren't many natural places to toot your own horn the way you're trying to do it.
5) Your chances are ok - they're not great. You're targeting 3 of the top 5 schools and 2 with notoriously low acceptance rates. Do you have a shot? Sure. Should you apply? Yes. But all of them are stretch schools. PS - can't hurt to bump up that GMAT if those are the programs you're looking at!
6) This is a case by case and school by school basis - no one answer fits all.
If you want to chat in more detail,
[drop us a line]!
Hope this helped,
Bhavik