I still need to play with it a bit, but I'm currently doing pretty much what heltonbiker suggested - bungee-ing the wheel of the kids bike to the rear rack:
The top of the kids bike wheel is strapped to the rack, and the front of the wheel is strapped to the frame of the towing bike. You can't see it clearly in the pictures, but the fork of the kids bike sits against the rear stay of the rack, so pulling the front of the wheel into the frame of the tow bike keeps the wheel away from the wheel of the towing bike.
Another variation that worked quite well has been to use a metal hook (similar to this, but one side is large enough to fit the wheel) to hang the wheel of the kids bike from the rack, then a couple bungee cords to hold it tight.
This works well enough for my purposes, but it's not perfect. Because it's the wheel of the kids bike that's strapped to the rack, there is some freedom for the rear of the kids bike to move up and down, which is good.
But because the bike is tipped up and off-center, interesting things happen going around corners. Turning to the left, no problem. Turning to the right... the rear wheel of the kids bike "flops" to the right and ends up about a foot off-center to the right. It comes back inline with the towing bike when you straighten up, but you have to have the cranks in the position shown so they don't come close to the wheel of the tow bike.
Another issue that came up after I actually tried it with my kid on the back of the tandem is that the kids bike has to be attached as far back as possible on the rack to give enough clearance for the stoker's heel.