I can often pick up flights from Syr and Roc into LGA for much cheaper than the change fee - idk if that's the case for DTW. I've found though that lower fare buckets often close on LGA whereas JFK is still available. So right now arriving in LGA costs ~$100 more than arriving into JFK.

Also might be worth the call in to see if delivery counts as hospitalization for medical fares
http://www.delta.com/content/www/en_...s/medical.html