We are just about to close on a house in the Woodcrest neighborhood in Cherry Hill and I went through the same questions you are going through. Are you guys just moving to NJ? We are and I'm getting kind of sad looking at the homes we missed out on buying due to me just being intent on staying in a good elementary school district.
Where we live now I had to play that game of requesting my son to go to a school outside of our district every year and it was nerve wracking and annoying at once. So when looking for a home in CH, I just wanted somewhere I knew I would be zoned for a great elementary school without question. I'm just going to throw this out there: we are zoned for Woodcrest (excellent school) but I really loved, loved, loved a house that was zoned for Clara Barton - which had terrible ratings and just didn't seem as confident in offering a positive experience. I really hope that I made the right decision and I hope you will too!
You can definitely request entry to an out-of-zone school but the other poster is right, they will only grant the request based on space for that year - although they will give some consideration to kids who've been there.
Anyway, it seems like we're on the same path - much luck to you! If you need to find new friends when moving there, let me know