My 2 cents:

Studies have shown that taking the GMAT each successive time will not drastically improve your score unless you really study and master the fundamentals of it. To me it sounds like you are rushing to get your app in ASAP, leaving you little time to prepare for it.

Your gpa is also lower than average, so the mix of GMAT and GPA is below average for Columbia and Harvard (though the engineering would be taken into account, as well as all quant-oriented courses you have taken).

I'm not too familiar with the Texas program but I know they are big on the oil industry, and that may be your best best. Columbia and Harvard would be reach schools, with Haas slightly below that. I would concentrate on Texas as your goals are more oriented for the school's program.

Hope this helps.

Here is what i would do if i were in your shoes:

1. Will stop the GMAT spree and focus my efforts on applications.

2. Will try to push in atleast 2 applications for round 2 (hope you have done the ground work - an outline of the essays etc.)

3. Will not apply to Harvard as the school is very very selective. My strategy would be to stick to schools that are more receptive to low GMAT scores (although Harvard is very receptive its selectivity is the concern here).

4. Try hard to secure an admit from atleast one school, and then take my shots at the big guns in round 3.

Now here are things that are working for you:

i). You are bilingual
ii). You have a very unique (and good) work experience and schools dig that!
iii). You have a decent GMAT score (6xx are pretty decent is your other parts are good - essays, recommendations, work experience etc.)

Now you might need to find some fall-back school also to apply to in the second round this is to satisfy points 3. and 4.

McCombs is a very good school and i think they would like candidates with unique experiences like yourself.

Hope this helped.
All the very best.