At that price point I think the only automation you'll be able to get would be mute automation. For motorized faders, etc. on an analog board, I'll take a wild guess and say you're looking at somewhere between $25,000 and $30,000 minimum - but I'll freely admit i haven't researched this in close to ten years (I remember something around #30,000 that fit your description from either Soundtracs or Soundcraft, can't remember which...), so there may be something out there i don't know about. The problem is most of the manufacturers are focusing their R&D for inexpensive consoles with lots of features to the digital realm.
You may want to talk to someone at Pro Audio Design (Rockland, MA), or some other place that specializes in selling new/used consoles to see if something like what you describe even exists.
I suspect in the end you'll have to choose between the analog sound you want, and the digital features you desire.