Why not try for a CM dinner? The night of the B-day...

I'm assuming you going to need a place to eat anyway...Give it a shot...If no ressies are available, then just wait till the day b4 and try again. Typically this is where some times open up, becaue people have to cancel 24 hrs. in advance.
I like that you've added the extra day..It'll surely help you out tremendously.... Have a great trip!