This thread is great!
First off, I think you need to determine how long it will take you to eat six big macs under the best of circumstances with no running. How long the "best case" takes would greatly influence strategy.
I am suspicious of the eat-run-eat and eat while running strategies. The look really good on paper, but I have to think that a stomach with 2,3,4+ big macs in it will make even a very easy pace feel much harder than it would otherwise. Plus, if you could hold the pace, I think a Reversal of Fortune could be very likely.
Then again, the body can handle what it's used to. As long as you put in some decent training for whatever method you choose, you should be fine. You have enough time to prepare.
This must be captured on video and posted for two main reasons.
1. For my personal entertainment.
2. You just might be able to get some weird endorsement thing from McD. It could happen. They're trying to pretend they're healthy now because they offer water and apple slices. Some fit guy approaches them with proof of a feat like this... who knows? Stranger things have happened. That Jared guy lost a bunch of weight and got serious cash from Subway.