Improving my PhD application for math programs
In reading through your comments, I couldn't help but get the feeling that you are "all over the map" when it comes to what you're looking to do in graduate school. If this is similar to the way that your personal statement read to the committee, it could help to explain some of the challenges you faced in applying to graduate schools.

For instance, after reading what you have written, I can't tell if you're looking to do algebra or bioinformatics—or if you're in an "I'm happy with either" situation. If it's the latter, this can make it harder for a committee to accept you: algebra readers might think they'll admit you, only to have you wander off into applied math, and vice versa. You may find it better to concentrate on one area—or, better yet, show how the different topics you're interested in are actually related to one another.

Another potential issue is the quality of your letters of recommendation. Is there anyone who can help you to evaluate your letters for you? Some colleges have career offices or academic counselors who can comment on the suitability of your letters for different kinds of programs (academic, industrial, etc.), although they probably won't "rank" them for you. If you had a very late letter, it's a good question as to how helpful it would have been, even if  it was from a big name (or perhaps that should be "in spite of" it being from a big name).  By this, I mean that the letter would only have value if it actually discusses your talents and skills in a meaningful way. A pro forma letter isn't all that helpful, particularly if you are from an "unknown" program. (This latter can also make your job tougher, since your school might not have  a track record at many graduate schools).

Finally, it also sounds like you have a rather untraditional academic history. This needs to be explained clearly somewhere on your application, in a way that shows thattaking you into a graduate program now would not be a risk. (Not doing this could again feed into the notion that you're flittering around from one thing to the next—which is not a good impression for an admissions committee to have of you.)