You might consider applying to Duke's masters program in stat and econ. It is a rigorous program and you can build up a better profile by taking PhD level courses. Duke also has a strong stat department, especially if you are interested in Bayesian statistics. In terms of math, I think you have taken more than enough to apply for econ PhD programs.
You are correct that your background is plain. And frankly speaking, I don't think your rec letters will make you stand out in econ applications.