Have you ever found that when you have a small amount of time to get something done, you're more motivated? This is certainly how it works for me. I used to block off whole days to get assignments done or designate a whole weekend to cleaning out the shed. But really, when I am pressed for time, I'm more efficient.
When I was writing my book, Funded!, I gave myself half an hour to write every day. Within that half hour, I aimed to get 500 words written, but if I didn't get exactly that amount, I wouldn't fret. The next day, I would come back and do the same. Had I given myself an hour (or two) to do the same task, I would have sat there not working for half the time and then at the last minute, cranked out the daily limit.
As my mom says, nothing would get done if there weren't deadlines. And it's true. So if you're looking for time to work on an application (or do the research for your perfect fellowship), give yourself a strict time limit. Designate twenty minutes a day, or use the twenty minutes between tasks to fit in some valuable fellowship time. Giving yourself all day to do this, or worse yet, waiting until you have a whole day free, will get you nowhere. Start today and take just a few minutes to get the ball rolling. Tell me how it goes!