This is very helpful. Attending an LAC will not hurt your MBA pursuits. Many LACs are well known and respected by graduate schools. Many students interested in business major in economics or finance at LACs.
With LACS, be sure to show a lot of interest by contacting the admissions officer this summer or early fall, asking for an interview via skype, and making the supplemental essays very specific to what the college offers and why you are interested.
I think you are on the right track with your list and your definitions. However, since you don’t need aid, I think Georgetown, USC, and Carnegie Mellon are high reaches – but it’s not out of the question that you’d be admitted in my opinion, though I’m not truly familiar with how much harder it is for international students.
The key is is have a balance of reach, match, and safety schools. And with top schools it is a numbers game so while you don’t need to apply to 20, applying to 10 or 12 is not a bad idea if you have the bandwidth to do that many this fall.
You’ve had some good suggestions so far. Here are some others to look at, though these are not safeties.
LACs:
Grinnell – they have a goal to be 20% international within a few years and they have a large endowment with a lot of resources. It is in isolated area, however, and cold in winter. High match?
Davidson – in the South, top 10 LAC and has a lot of students who go into business. Near Charlotte which is a major banking center in the US. Reach.
Claremont Mckenna in California – also a top 10 LAC. It’s known for economics and students on business track. Reach.
University of Richmond – This was mentioned already, but I think would be a good match for you – warm location, strong business program.
Mid-sized:
Duke-- in the South. Sends lots of grads to work on Wall Street. High reach.
George Washington and American – both in DC so mid-Atlantic coast. GW is more urban campus and American is on the edge of the city with a more traditional American campus feel. Reach.
Rice in Texas and Tulane in New Orleans are both somewhat like Emory and WashU so you might want to look at them. Low reach perhaps?
Bigger school:
I suggest UNC partly b/c it’s my alma mater (!!) but also because it has a top 10 undergraduate business school in the country and is located in the South. It is larger – 16k undergraduates - so might not be your cup of tea. High reach too b/c it has cap on students from outside of North Carolina, but it’s a great place! 
Again – I don’t know the international admission rates as well but I hope this helps. Good luck!!