Do you really need all 16 days with dining?
Here's what I would suggest:
(1) Book a room-only reservation on your first night. Plan on hanging out at the pool or see Downtown Disney. You won't have a park pass for that day. This works out very well if you are getting into Orlando late in the afternoon or in the evening. You will be able to use a discount like
AAA on this room night.
(2) Expand your current reservation to a 14-day reservation. You can "connect" your room-only room with your
free dining room so you don't have to move. We did this in August of 2006 when we arrived the day before free dining started

.
(3) Upgrade your 10-day hoppers to Annual Passes. I'm not sure if you can do that at check-in or if you have to do it at the park. Either way, it's not hard and it will save you a bit of money:
10-Day Hopper: $277
5-Day Hopper: $267
Total = $544
Annual Pass = $462
(4) Add another room-only to the end of your stay and "connect" it like you did the first night. You can get this room at a discount like AAA or the AP discount now that you have one

. Your dining credits will expire on the night that you check into this room, so you only have to worry about purchasing meals on the day that you check-out. This works best if you are leaving Orlando in the morning or early afternoon.
(5) Feel the burn of the Annual Pass in your pocket and plan another trip within a year, LOL! Ooops! That doesn't save any money!
The alternative is to book two consecutive free dining reservations and connect them so you don't have to move. Or perhaps change resorts part way through your trip. You must purchase park passes for each reservation, so it would cost you approximately $550 for park passes. Here is a link to park pass prices:
http://www.allearsnet.com/pl/ticketchart.htm