ADRs (advanced dining reservation) can be booked 180 days in advance, so next week would be too early for May. When you make your hotel/package reservations, ask the cast member what is your 180 day mark. For reservations at Cindy's, you will need to call on that day at 7 am eastern time. If you don't get the reservation, keep trying. Something might open up.
At your 180 day mark, you can book for up to 10 days into your trip (180 + 10), so you can make all of your ADRs on the same morning.
We honeymooned there in 1997, and we ate at Cindy's. It was nice to be inside the castle, but it was overrated. If you go, just know that you are paying for the atmosphere and the characters if you go to a character meal. Currently, dinner is the only non-character meal.
Try California Grill - you have a beautiful view of the castle and the food is great. If you can find out what time the fireworks are and you can get an ADR about an hour before, it is a great view. Even if you don't get a table next to the window, you can still see the fireworks over the castle. It is beautiful!
Enjoy your honeymoon!