I would definitely not reapply and go to NYU. I have a friend that went there and wished they never graduated. They loved it.
Additionally, the tuition at Case is $321,872 and NYU is $313,718. These are cost of living and tuition estimates that I got from each school. Therefore, it looks like Case really is not cheaper than NYU anyway. Plus, NYU you'll have a great experience living in NYC.
Military is a great option if it is something that you are interested in. If you're in it just for the monetary compensation, then you'll hate it. If you're interested in serving your country while doing something you love in practicing dentistry, then you'll love military dentistry. If you're at all interested in Navy dentistry, then contact a recruiter and have them set you up with a MEDVIP trip. This is an expenses paid trip to San Diego to check out dentistry in the Navy, plus it's a great time.
If military is not your choice, then you can look into public service dentistry as a way to not pay the total cost of your education. Your options are:
1) Working in a low-income Community Health Clinic. This option under the National Health Service Corps will give you $50,000 tax free toward your loans for 2 years of service. You'll be paid by the CHC and make a decent living.
2) You can work in any dental job for the government (IHS, military, CHC, military civilian dentist, etc) for 10 years, and whatever you have left on your student loans is completely forgiven. This can also be combined with the 25 year income contingent plan, which will stretch your loans out to 25 years and your payment will never be more than 15% of your total family income. (Note: The new education act that Obama and Congress just enacted is trying to be changed to 10%). Depending on your family situation post graduation and lets say you start out at 100k a year, you'll be paying ~$1400/month for 10 years. (~$140,000) Note, these are rough estimates and don't factor in a lot of things (i.e. inflation, tuition rate increases each year, etc). You can more accurately track your situation at:
http://www.finaid.org/calculators/icr.phtml
Make no doubt, dental school anywhere is expensive. But if you're willing to consider other routes besides just private practice, then you'll not be paying that full tuition bill. These are just some things to consider. Just remember that no matter where you go, you're gonna have Dr. in front of your name and you'll be able to practice dentistry.