The way to do this challenge is what the PBR guy posted - breaking up your runs into smaller chunks just means running starts to interfere with drinking, and you are stumbling around. Good for a story, but this challenge requires a considered, thought-out approach to finish.
You might think 25 miles is a lot, and if you think about it in normal running terms, it is - I was always pretty dead after my 20 mile weekend long runs. But here is the key - I was doing those runs at around 6:30/mile pace, getting faster at the end. For this challenge, I'd be running my 25 miles as slowly as I wanted. I'm guessing this would be around 8 min/mile the first day, getting consistently slower each passing day. As a last resort, I'd cut the run down to 18-20 miles, and make up the miles in 1/2 miles chunks throughout the day or in the 4 hour "home stretch" after the end of the 4th day.
After each morning run, I'd sit down to a huge, greasy, delicious breakfast to help buffer the alcohol, and start my drinking. I figure waking up at 8 gets me finished running by 11-11:30, and eating by noon. I then have 14 hours to drink my 25 beers. Easy right?