Marine Benefit Extra: 27820 Graze
As far as I'm aware, this is a world record, despite me screwing up a bunch of times (in particular, I really should have suicided around 7:07, and bombing around the 17:53 mark instead of accepting the death probably cost me about a thousand graze). That's the good thing about this game not being as popular as it should be: world records are, right now, relatively easy to set. I'm sure someone could make 30K if they really cared to; in fact, I probably could myself, if I'd time out everything instead of skipping the low-graze stuff.
Credit to SomeGuy712x for several of the strategies used here (especially Mikoto's third card) and for inspiring me to make this run in the first place. Video in question is here: http://www.youtube.com/watch?v=WDnNfVtWUbg
UPDATE 10/06/2012: Well, that didn't last long. Record's been shattered by a mile - by a difference of exactly 13500 graze, to be precise. See video responses for the new WR in question. I'm not inclined to try to beat that score anytime soon, so right now I'll just congratulate the new record holder on the achievement.