A very interesting dilemma. I find it odd that the Academic Board would not have known that all the Foundation slots had been filled. Also, the number of slots available is not cast in stone, so exceptions maybe could have been made. Your BGO will know your status. Call him.
If you were recommended for Foundation, this means the board most likely found you not scholastically qualified. There are about 500 3Qed standby candidates ahead of you in line who will be offered appointments before you so I would say right now that your chances of USNA this year is 0% instead of 1%.
If you decide to go the 'wait-a-year' route, I would have a long talk with Capt Wallace at the Foundation. As a non-funded candidate, will they assist you and 'guarantee' you the same basic offer as those who they fund? If not, a year at the local university, taking NROTC if available, and courses to mirror plebe year might be the best alternative. Without the guarantee, getting on with Plan B might be prudent.
The vast majority of Foundation candidates have strong packages but are weak either academically or with standardized tests. A call to the CGO can help you here. In any event, conversations with the Foundation, CGO, and your BGO are definitely in order.