Just go on the other side of the table, maybe?
Chess board Rotator!

You could always just get a lazy susan, though it probably wouldn't have a locking feature or anything.

lazy susan. could simply add a little peg to stop the swivel (although that would me you could only spin it in one direction).

This isin't exacly for this but it does the job and very well at that: a rotating low-profile cake stand. Just put the board on top of it and problem solved- you can rotate your board at will, and this is very cheap I saw one for 10 dollars at amazon.com>>http://www.amazon.com/s/?ie=UTF8&keywords=rotating+cake+stand&tag=googhydr-20&index=aps&hvadid=4644899247&ref=pd_sl_411y4rvw4p_b or go to your local cake supplies store they might have it even cheaper.
you probably want to do your analysis away from your computer but just in case you haven't seen this:
http://www.chess.com/analysis-board-editor.html

Thanks for the suggestions.
I'm running Fritz in Infinite Analysis mode, off the database, and sometimes like to have a board and pieces up when I'm going deep into a game. And I find that appreciating the situation from both sides of the board, with ease, is very helpful.
I have the setup on the board as the fixed variant. Then I use the variation board in the engine to go through suggested lines, with the fixed variant as reference; and then I can go look at similar games through the database.
Went through the ones on Amazon, and found a rotating tv-stand that was only 2" high, most of the cake stands were at least 2" higher. Thanks for the tips!
I like using a board and pieces when doing my analysis, but it would be great to have a simple pivot under my board, to let me rotate it from white to black with ease. Ideally, I'd like it to have a little lock when it reaches the correct position.
I'm pretty certain something like that's been made, and wonder if anyone knows where I can order one.