Assuming you can get 720+ on the GMAT, you look like a good candidate for those top 20-40 schools you listed. I would even shoot into the 10-20 range. Here are my comments on the weaknesses you listed:
- I have little work experience with a large company. - Not that important. You have a CPA from your country and a little experience.
- I can still improve my quant and econ background. - Taking econ stats and econometrics could be useful. Overall, your math background is pretty good for what you are aiming at. I assume you are looking at doing archival research.
- My masters isn’t a MAcc like those of most accounting PhD students (I don't have the resources to pursue one) - A MAcc isn't actually that great of preparation for an accounting PhD. Knowing the financial accounting rules is good, but your CPA implies that you have that. The only reason I would recommend a MAcc for you would be to address point 5.
- I can improve my GMAT (working on this) - Yeah, higher is better. Make sure you can get 50 or 51 on the quant and as high as you can on the verbal.
- No rockstar LORs - I think this is actually your biggest problem, and I'm not sure how to address it for you. I assume the top school in your country has researchers. Did they at least do accounting PhDs at decent American (or possibly top international) schools? That would help a lot. Can they realistically speak to your ability to do accounting research? Do you think you could reach out to an accounting professor or two at your master's school? You could give them a brief background (a little less than you wrote here) and mention that you were a student there and are interested in accounting PhDs and ask for their advice. The 3 schools you listed all have good faculties and PhD programs, though CMU has had some issues.
- Little research experience - Most people don't have much research experience going into programs. You have some exposure. Look at newer issues of TAR, JAR, and JAE to get an idea of recent research. SSRN is a source that is actually more up to date. The fact that you know earnings management and disclosure shows you have at least some exposure.
I hope that helps. I can answer more questions or give more detail, but I don't get on this board as much as I used to.