Continuity is less about individuals than it is about systems and the organisation of information.
This means that the system must be defined. Definition does not imply limitation. It is important to know how new projects are organised, run and scrutinised without declaring what they should be. How far one goes with the hierarchy is also important. Are different language versions or large sub-projects of a common project different projects? Many "embarrassing" moments have come out of English content wikis. How many potential pitfalls are waiting in other languages? How feasible is it to have language experts for each of the wikis? Recognising limitations inherent in the system is also important - these should be declared.
The professional project manager can still be a volunteer. There are large numbers of astonishingly talented people willing to work for free for causes they believe in. The difference between a volunteer and a "professional" is not about paid / unpaid it is about the time dedicated to a project and their accountability. Some projects are large enough to require full-time commitment. Project managers must accept this and be responsible. Not all the things that need doing are glamorous.
Project management may not be about content generation alone. It is also about budgets, settling disputes and being responsible and answerable to the organisation at large. If something goes wrong, they must sort it out immediately and understand and report back on how it happened. They are also there to find their own successor.
There must be a project log, and project manual that details exactly how things are done (thus ensuring a consistent approach). Clearly the manual can evolve but it must be the DNA for the project.
A simple project blog or mailing list isn't good enough since the quantity of information produced (and the various diversions it follows) makes rapid decision making impossible. In reality, each project needs its own moderated (and access limited) wiki where the basics are paired down: how things are done, daily / weekly / monthly ... tasks, etc. At the moment projects may be run by the person who started them or someone one or two iterations away. What happens in 50 years?
The organisation itself requires a similar approach with a slightly larger set of responsibilities: PR, legal, accounting, admin and an overall director. These are the trappings of any formal development organisation. Having them doesn't limit the activity of the volunteers, it is simply a responsible way of handling information generated by the organisation.
The director also needs feedback and that will come from your board.
Each of the tasks can be defined and each of the roles can be filled. A mechanism for recruiting and training new people to fill each task is much more straightforward when you know exactly what that task is.
I would imagine that a simple flow could be as follows: volunteer works on a project, gets more involved, gets groomed to become the project leader, stays in that for a year and grooms his / her replacement, gets invited to join the core team, gets groomed to become director, serves for a set period, becomes a board member. Some of these tasks are full-time, some are not. The person accepting major tasks does so recognising what the commitment is and what it will cost them (if the tasks are unpaid).
This is continuity. It doesn't limit the content, projects or creativity of the organisation. It channels the most capable people through a system that maintains the integrity of their knowledge while still allowing the organisation to evolve and meet future needs.