Much as I hate to burden you with the task, the only way to insure that the seedlings won't survive is to pull them out by the roots. Make it a week-long chore, rather than going at it all at once. You might want to water the area the day before y ou start pulling. If you just cut seedlings back, they will most likely resprout. At any rate, roots will still crowd the area and digging made difficult. As for the idea that leaves can somehow transfer that nitrogen to your soil. Yes, if you compost them, there might be some positive use for the compost. However, nitrogen is not a super-long lasting chemical and the idea of leaving the leaves to gain a fertilizer effect is not a good idea. Good luck with pulling!