I don't know why you would think you have to fly 300NM away from your start point. Three 100NM legs is just fine. It's what I did in the end for my official one. But as shunter says, you're supposed to like flying. Go and fly a few of them.
As for doing it in 24 hours. I know of a current airline Captain whose 300NM cross country took three days. I was with him. It was kind of an extended pub crawl. Do you think I should turn him in?