I board my horse at a nonprofit mutual benefit corporation. We were having a members meeting to discuss issues with a board member’s unacceptable behavior and found out that the whole board is quitting. So we turned the meeting into a “who-wants-to-run-for-office” meeting and took the names of people who want to run. Our main question is how do we legally throw a board together by the time the current board quits? The bylaws do not say anything about an entire board quitting. I'm afraid we will lose our nonprofit status or worse. We are just regular folks who don't have a lot of money, we just love our horses.
Your bylaws probably don’t say anything about replacing an entire board because it is pretty unusual for an entire board to resign at the same time. I wouldn’t worry about losing your tax-exempt status, however, because your members have the ultimate power to run the organization and it will continue in existence doing what it always does during this interim period. You should call a special meeting of the members to hold an election for new directors. If you have to replace people whose terms expire in different years, you can provide that the people who get the largest number of votes will serve for the longest terms so that your new board will have appropriately staggered terms. You are lucky you seem to have enough people to run to fill the seats. There are a lot of organizations where it is very hard to find people willing to accept responsibility.