My own suggestion would be that a treasurer who is an appointed Board member would need to face the electorate not less than six nor more than eighteen months after that appointment. The six months should be enough time for him to put his mark on the job, and show that he can communicate with the general membership.
Why would an appointed member ever have to seek election? The point of appointed members is to get people with specific skills the board requires, the point of election is to get people that can represent the community. They are distinct goals, and you shouldn't try and mix them. (Of course, if a member of the community has the required skills and can fulfil both roles, that's great.)