I guess you have a good background in math. But I can not see Multivariate Statistics, Bayesian, and GLM(or categorical data analysis) in your coursework. Some computing courses on SAS, R, Python, and Database might help too. If you are worried about the reputation of your school, having extraordinary LORs are really important. Seems like your GRE scores are high enough to not be automatically screened by the top 20 schools. For SOP, you can refer to here. If you write an excellent essay with the fine language control of English and find a perfect fit for your interests, then you can also be one of the top choices for the programs. To sum up, I highly recommend you to take some more statistics courses and contact your alumni who got into the top statistics programs ASAP. They could recommend you some professors you can ask a help for.