I can write (although my ACT and SAT would say differently), and a majority of the things I write I don't bother to draft, but it is not something I enjoy. I used to read alot, when I was really young, but I got made fun of for being the only person who could read in my class for years, and I stopped. I have terrible grammar, but for the years I should have learned all those things I went to an alternative school where nobody believed in trying, or teaching. I just got back into reading a few years ago, and I'm still having a hard time remembering to bring my book everywhere. I don't think reading has helped me, I failed english my sophomore year (in highschool, and it was because I never turned anything in, not because I couldn't write) and they put me in a remedial reading class ( I guess if you don't write your not supposed to be able to read?) I took the initial reading comprehension placement and got out of it. I have never understood the structure for writing, it doesn't make any sense to keep saying the same crap over and over and over again. This post is longer than a majority of my papers.
I may not be helping, but I think all you really need is practice, reading just gave me therrible vocabulary I have. One technique I use when I bother to start writing my paper in a timely manner is to write it, as best you can, and then pinpoint a certain phrase that doesn't sit well with you, and change it, and then look at everything else and make sure nothing is conflicting and that it flows ok, and then move on to another phrase that just doesn't look right.