This is a great thread. Easy to ponder over this one quite a bit.
I would wear a pair of running shorts and medium weight goretex pants. Also a light weight goretex t-shirt and a medium weight goretex jacket that had plenty of pockets. I'd wear running shoes (obviously) and also have a stocking cap. 45 degrees is cold enough that you would need to be well covered. And then I would sleep under the clothing during the middle of the day.
For food and liquid, I would try to carry around 8 liters (around 2 gallons) of Gatorade. I would get 2 of those Camelbak's, wearing one on my back and one on my front. I saw ones that carry 100 oz each, have room for extra storage and only weigh 1.6 pounds empty each. For food I would bring 30 Powerbars and 20 Gu packets, fitting them into the packs. Also I would bring 2 decent sized (each 24-32oz - around a liter) water bottles with Gatorade I would carry in my jacket pockets. I figure the Powerbars and Gu would weight 6-7 pounds, 256 oz of Gatorade would weigh around 16 pounds. The weight of the packs would bring it to around 26 pounds of "stuff" not including the clothing.
3 miles an hour seems like a reasonable rate of travel. Doing this for 16 hours a day (6pm to 10am) would give me 48 miles a day. Walking steadily during the night should help limit the amount of fluid I would have to intake. I would drink about 64 ounces of Gatorade and consume 7 or 8 Powerbars and 5 Gu packets each day. I think I could do this for 4 days, covering between 190 and 200 miles. Finally, I think I would try to bring a picture of a really hot girl. For several weeks before I would look at the picture and tell myself she would be waiting for me at the finish. So, once I was 3 or 4 days into the trek and started hallucinating, I would start envisioning her, causing me to keep on going at all costs!
I had a question for jtupper. I would like to get rid of the weight loss restriction. Since this is all hypothetical anyways, I would like to be able to have people lose more than the 6% of their weight. If someone wants to push themselves close to death, more power to them. I think the only condition is that the person lives for it to count as a record. So, if you go 425 miles but die at the end, you lose. I know it sounds ridiculous. I am interested to see how far one could go in these controlled situations but have it be almost a life or death scenario where we see what is possible if you have nothing to lose. Is it possible for a person to lose more than 6% or 8% of their body weight and still keep going? I would guess that has happened in survival stories.
I think the best athlete for this would be a medium build ultramarathoner. Someone who ate a ton for a few weeks leading up to it, packing on an extra 10 to 15 pounds of fat reserves they could burn off during the trek.