Part of my problem is that I do not really believe in pure democracy
Democracy is a means to an end, not the end itself. First define what you believe are worthwhile values goals for you, for other individuals and then for the group.
I don't think ideas become good simply because you can convince a majority of one that it is so. Democracy tends to work in general over long periods of time. The chance that it will work for specifics at this time are dubious.
Which takes precedence, the individual or the group? (And by precedent I mean relative, not absolute). If you favor maximizing individuals self actualization, moral autonomy, self expression and so on, what system best accomplishes that. Again, I think you are elevating democracy and making it a moral value, rather than looking at it as a method of achieving other ends.
Oligarchies preserve the relations of power and favor the group over the individual. I don't favor rampant individualism but feel that the function of government should be to try to maximize each individual. The best way I can see to do that is a democracy that pushes the decision making to the lowest levels.
I'm not against oligarchies. I had a professor in a Political Science class who had us study the Swiss government as an example of a modern state that worked very well, and it was an elected oligarchy
In what sense does it work well. While Switzerland has one of the lowest murder rate sin the World (.2 per 1000) , it has a relatively high rate of violent crime (25 per 1000 I seem to recall), for example. First define "worked very well" and work back to what that says about your values. Is it streamlines and efficient? That would imply some level of enforced conformity. Federal Express is very streamlined and efficient. As long as you use their boxes and letter packs and follow their rules.
They are not self-appointed and need to be responsible to their constituents and to the overall polity to remain part of the governing board. Although an individual may be replaced, there is continuity because the real decision making must be done through consensus of the governing board.
And the needs, as identified by the governing board, become paramount. And often self justifying. Why is the continuity a good thing? How is the danger of stagnation addressed structurally? Is power actually vested in the permanent (unelected) staff?
How can real progress be made when we so consistantly reverse direction?
Define progress. Is retarding the government in it's attempts to curtail individual rights progress? Is promoting the free expression of artistic ideas progress. Granted, an oligarchy can do these things. A democracy has to do them.
Convince me that - other than being contrary to our democratic predelictions - oligarchy is not the way to go
Again, it depends on what your core values are. It has nothing to do with democratic predilections. Both democracy and oligarchy are methods to accomplish things.
I think the way to begin to answer your question is to explore what basic values you (and others) hold in common. Simplistically, take the Bill of Rights. Which system (practically) fosters those ideals best? (Over the long run). Which provides checks and safeguards to make sure those rights persist as a matter of necessity rather than a matter of convenience?