I agree with the others about EPQ not being worth it. I decided not to do it after speaking to students the year above me and asking whether it was worth the time, and they said no, and having not done it, I don't feel it weakened my application in any way. If anything, I feel it made my application stronger, because I had more time than my friends, and did other things and concentrated more on my January exams.
That doesn't make you OP, or me, any less passionate about our subject or anything like that. At the end of the day, getting into the best university that you can, IS a game, and you have to play it. Okay in an ideal world I would have liked to have spent time doing an extra research project, but in the real world I didn't have time for it and focused on other things. All schools structure their EPQ differently, but in my school, the time for submitting their EPQ reports, meeting with their tutor to go over their report, doing that presentation thing you have to do for EPQ, fell right in the middle of January exams, and I saw some of my friends this year having a hard time juggling both. It appeared to me, as though EPQ wasted a lot of their time. I don't think I saw anyone manage to do it in one weekend or ~10 hours work.
On my personal statement I neither had the space to mention an EPQ project, nor did I want to, as all my other things were in my eyes more important than any EPQ project that I could have done and mentioned on the ps. Yes maybe if you do do an EPQ that may 'sway your application in the eyes of the admission tutor and get you an offer', but then that could be said of anything and everything, such as, oh you should have done DofE gold, or you should have been head boy, that will work in your favour if there are two applicants both with AAA but you also have this extra stuff, etc etc.