We are a 360-member all-volunteer nonprofit 501(c)(3) in the South. We have a hard time finding people to hold offices. One reason is that we have many part-time (3-4 month) residents and we typically hold meetings from September to May. A similar organization "solved" the problem by allowing two people to share an office. Have you heard of this? And if so how would you word the bylaws?
You may be closer to resolving this situation than you think. Do your bylaws envision a vice-chair or vice-president who will act in the absence of the chair or president? Have you appointed an assistant secretary or assistant treasurer who can act in the absence of the secretary or treasurer? Do your bylaws or your state nonprofit corporation law permit the Board to appoint “other officers”? Organizations cope with absent officers all the time, although the anticipated absence is more often occasional than seasonal.
It is less frequent to have co-officers than vice- or assistant officers, but not unheard of. I was once on a board that had co-chairs (until a funder told us he would never fund an organization that didn’t have a board strong enough to generate a single chairperson as its leader). If your board selects the officers, you could probably select co-officers for any of your positions under the provision giving the board the right to appoint “other officers.”
It may be more difficult if your members directly elect the officers. The bylaws might have to be amended to contemplate co-officers and the way they would be selected. Do they run as a team, for example, or do the top two vote-getters share the position (e.g. Trump and Cruz)? Even if the Board is the selecting body, you might want to amend the bylaws to be specific about the right to have co-officers.
In either case, you have to find people who are willing to share the job, and to agree on each individual’s responsibilities. But there is nothing inherently wrong with the concept of co-officers and it may satisfy the organization’s needs when the snowbirds return home to the North.