You may actually be overqualified for some of the programs.
I got into a program after my freshman year with Calc 3, a semester of linear algebra, and a course in non-euclidean geometry under my belt (which i took for the sole purpose of getting a letter of rec for reus-because i had only one other math class that was a professor rather than a grad student). According to the people running it, they really wanted all the participants to have the same background - so it was mostly sophomores with roughly the same classes. The first two weeks were a crash-course on the relevant material, and if I had already taken abstract algebra the progression would have felt really awkward and remedial. I applied to lots of programs after my sophomore and junior years, and didn't get into any of them. My theory is that once you're through the standard algebra and real analysis sequences (no pun intended) and are taking graduate classes, there aren't as many programs looking for students like you, and those programs are much more competitive.
That said, keep applying every year. I can honestly say that the one I went to was the best two months of my life, not to mention that they pay very well (or so it feels to an undergraduate) and are one of the best things you can have on a grad school application, especially if they lead to a publication.
Another thing to take into account is that they all tend to accept 8-15 people out of often like 300 applications, so chances are, if you are totally qualified, so are 50 other people, so there's a lot of luck involved unless one of your recommenders knows someone in the program personally. To answer your original question, the advice i received on personal statements is to be pretty straightforward, but include a paragraph with something you are particularly interested in with some detail - demonstrate that you're really independently engaged and can understand and communicate mathematical concepts - but be prepared to talk about that same thing in an interview (I did a phone interview for the program i got into). Though I struck out two years out of three, so maybe my advice on statements isn't the best.
From what it looks like, as people have said, you have a freaking ton of coursework under your belt. Starting next year, it would look into trying to do some research at your home institution. See if there's a professor that could help you find an accessible problem or is working on something they think you might be helpful at - they'd probably be willing to give you course credit for it as an independent study.