Ok, I have to admit that I'm getting a bit bored with the idling drills, but I'm keeping at it. Progress isn't fast, but I'm not regressing either. My best so far is 8 cycles left foot down and 6 with right foot down. Still a long way to go.
The mental images that I've been using during my idling practice the past few days is to emphasize smoothness and rhythm through the whole cycle of the idle stroke, and to emphasize the backstroke.
The smoothness and rhythm image idea came from my realization that when I was doing the 100 or so idles using support I had reasonable smoothness and rhythm, but when I later let go and tried to idle as many times as possible, all that form went out the window and I just did whatever i could to stay on top and rocking. I suspected that would lead to bad habits, so now I'm trying to maintain the rhythm, still try to do as much idling as possible without support, but not hesitating to touch supports on either side that allow me to keep balance and keep idling. I think that learning to keep that rhythm will pay off down the road.
The backstroke idea came to me when I was flailing around trying to keep my balance. I found that I wasn't using the backstroke much to make balance adjustments, instead doing most of the shifting on the forward stroke. When I did use the backstroke for more balance, I had greater success. So now I make sure I carry the backstroke back far enough that my lower back arches a bit, and that seems to help.
I realize that all these mental images will be discarded once I get proficient, but for now, when I'm still struggling, it is helping a bit, or at least giving me something to think about while I'm doing the drills.