I am somewhat surprised that you have not been accepted anywhere. It is not your fault but probably the fact that you went to GW which is not considered to have a 1st rate classics department (actually it does not have a classics department but a joint department with other languages and this never looks good). In this case whatever your qualifications are and whatever good (rather best) things people have to say about you might not have as significant effect as in the case of someone who went to a 1st rate undergraduate department. It may well be that the current financial situation affected some of the fellowships too (I know from prof. Keesling that tenure tracked job advertised in September were canceled in November and there were about 8 such jobs left by December. That's down from the usual 40-60). An MA might be a good idea but note that most first rate programs tend not to give fellowships in this case. Most people in your situation would go to a post bacc. program.
It is shorter, less expensive, and if the program is good (e.g. Penn) it helps one get into a good school. The problem is that you are such a good student that it will probably feel like a waste of time.
So, that makes me feel a little better...