Hi, Christi!
This is quite a decision to make! Dinner at Be Our Guest Restaurant is delicious. The theming of the restaurant is amazing, and meeting The Master is very exciting, indeed. (He is huge!) While The Beast is normally there during the dinner hour, it is not a guarantee. There is a PhotoPass photographer in attendance during dinner to capture your memories of meeting The Beast.
By visiting Be Our Guest Restaurant during breakfast, you still get to see the amazing castle and stroll through The Grand Ballroom (my favorite), The West Wing, and The Castle Gallery. However, you are correct you will not have a chance to meet The Beast and there is not currently 'Grey Stuff' on the breakfast menu.
My personal opinion would be to keep your breakfast reservation and make other arrangements for dinner that night, such as a Quick-Service meal. Time goes so fast for me during special events such as Mickey's Very Merry Christmas Party, and I never seem to have enough time to accomplish all I want to do and see during them. I would keep trying for a dinner reservation for another night during my stay to meet The Beast and to try the 'Grey Stuff' (it is delicious). As other families make changes to their plans, reservations may become available as you get closer to the date.
Wishing you and your family a magical vacation, Christi!
~Rachel