If you are going to delegate roles on the forum for the existing administrators, often with overlap as you said, any elected administrator would often be left with nothing substantial to work on other than being an individual voice of community concern. And even then, it really does not matter what they say as the other administrators are of a certain group. What I mean by that is the core and appointed administrator all share a similar mindset, and to have anything as a major issue according to the compact, you need two administrators.
The idea could work so long as those who were accepted to be nominated were not weeded due existing administrator concern over irrational pasts or community fervor of putting the popular person on the spot. Trying new things isn't bad, but meh. Three months is also a lot of time on an online forum - the only thing a person would have to learn in possibly how parts of SMF work, but that's easy enough. I would assume four months would actually be a better time frame as six months would be a little too long - and four would be a little more.