Here's an update, in case anyone's interested. I've been cutting through the local mall's parking lot for about two months, since I first posted this, and I have to say it's actually working quite well. To be more precise, I don't actually drive through the parking areas, but just on the roads that connect them to each other and to the public road. I do this because the main road next to the mall, which I would otherwise have to take, is shoulderless and congested.
In the mornings, between 8 and 9, the stores aren't open yet and there's hardly any cars around at all. I can see for hundreds of yards in 360 degrees as I approach the stop signs, so I don't usually even need to stop.
In the afternoons, of course it is busier, and I do have to pay attention, and at least slow down and be prepared to stop at the stop signs. But the good thing is that the cars are not going any faster than I am, so there's no problem with taking the whole lane at all times for the best visibility. It's even kind of a good way to practice VC skills, because you can ride vehicularly just like on a real road, but the traffic is slower than on the road, and there is more time and opportunity to practice your negotiation with motorists and pedestrians, with less pressure and risk. And where I exit the mall lot onto the main road, the light cycle often works out that I can make a right turn and immediately get into the left lane for a required left turn with no overtaking cars to negotiate with, an unexpected bonus!