Hi there,
Congrats on the great feedback and reviews you've been getting professionally. Overall yes I think that is a great sign and should help strengthen your candidacy. Certainly while most recommendations (for b-school) are fairly similar/positive/standard etc, a GREAT letter that really makes it clear that someone thinks you have clearly excelled above and beyond your peers can make a big impact (and an 'average' letter will not necessarily say that). Encourage your recommenders to aim to 'categorize you' or compare you to your peers (as in, top x % of those they've supervised etc), and to support their statements with specific examples and stories that illustrate your strengths... the motto of 'show, don't tell' the reader is really useful for recommendations.
To your specific questions:
1) Most of my projects have been 4-8 weeks. OK to get recommendations from someone who has only managed me for that long?
Often typical in a consulting role; all you can do is your best in terms of assessing who will write you the best letters, considering supervisors that are usually shorter term, and anyone with more of a longer term relationship if applicable.
2) Is there any strategy to get recommendation letter writers to include this high praise in the recommendations?
It's great to provide as much useful info to your recommender as is possible; copies of what they've written about you in the past for example can be useful; summary/bullet points about what you worked together on or examples/stories etc can be useful; your resume; even quick bullets about 'why the MBA' and 'why this school' can help.
3) Will it have high impact, given most recommendations are probably strongly positive anyway. Any way to set myself apart?
(Addressed in my paragraph above)
4) Anything else I can do to show my strong performance (mention consistently high review scores, %ile etc.?) Where?
Potentially on resume.
5) What are my general chances (profile below) - targeting HBS (top choice), Stanford GSB, Wharton
In terms of overall feedback, you have the basis for a strong profile, and I like the insight you've shared here about what influences you; how the international experience affected you, etc... aim to share that level (and more) of your thinking and your learning and what's influenced you in your essays and applications to further personalize your apps and really share who you are. Anyway the challenge is just that those schools of course are SO competitive...

so no guarantees as they do turn away a lot of highly qualified applicants every season! It will be tough; anything you can do to stand out from your peers (those most similar to you) and to show what you'll bring to the class; demonstrate your leadership and teamwork skills; show why you NEED the MBA; show how well you know the school and are a great fit for this program in particular... will all help. For best chance of getting in overall you may want to consider applying to a few programs outside the top 8-10 or so, just fyi!
6) Company does not officially sponsor until after acceptance, but I have been verbally told I will be sponsored. Where can I show this?
Obviously don't claim it as definite if not but you can honestly share what you've been told in essays or optional essay, and/or interview.
Good luck on the process, and keep us posted on how we can help!