Rob, the way I always fish eyes at night is slow trolling floating stick baits. If you can't troll slow enough going forward try back trolling.
I usually use either larger sized floating Rapalas or Husky Jerks. Sometimes the jointed ones work better for whatever reason.
Either use a Rapala knot or a cross lock snap so the lures action won't be impeded.
I also sometimes play with the eye of the lure a bit with pliers. If you bend it down slightly you'll get a much more erratic action.
A lake like you described I'd first key on any windward shorelines. At night troll as close to shore as you can without getting screwed up. Beyond that any shoreline that has visible rock should be good. In that type of lake rock sticks out like a sore thumb and attracts fish like a magnet.
Also, in shallow, reedy, dishpan lakes many times I've found walleye by looking for subtle reed points.
If reeds is all you've got look for any irregularities.
Good luck!