Thank you for your quick response.
Yes, our bylaws are specific in defining a quorum as 4. Board members are elected annually by the entire association, with 3-year terms so approx. 1/3 of the board is re-elected each year. I believe our Declaration does allow for special meetings to be called, either by the board (which probably cannot do so without a quorum), or by a specified percentage of the membership. Our remaining 2 board members want to make appointments to hasten the process, but I'm not sure if they can do this. Ultimately, I think we need to amend our bylaws to account for this situation, but right now, we're in limbo. I feel the proper solution is to call a special meeting with whatever notice is required in our governing documents and hold an election at this meeting to fill the vacancies until our next annual meeting, in September.