I'm not a published writer, but I'm quite good at academic writing. I have two university degrees and a Graduate Diploma, and I am studying a Masters of Teaching currently. I teach ESL, so I'm very good at picking up grammar and word choice errors. Much of the ESL I teach is for University preparation, so that also helps me with essay writing.
It's hard to quote accurately for this project since you don't say how much to charge, but I would expect to charge for about one hour per 1200 words.
I can only proofread English, so I'm not suitable if there are substantial non-English portions.