Thanks for the replies, guys. I think the balancing guy worked it out, though I have yet to road test the job. There is less than a third of the original quantity of weight on the rear wheels, which looked so wrong before. He spent two hours trying to get them right, and modified a couple of his adaptors to make it work. He seems to be a technician who cares, and took the time to sort the issue. The icing on the cake is when I showed up at the end of the day to pick up the wheels, the counter guy had already closed off the till, and so charged me nothing for the job. If the job is done well, this guy is getting a coffee card and an 'atta boy' call to his supervisor.
I think the next time I have all four tires removed from the wheels, I will have some minor machining done to the centre hole on the back side of the wheels, and make a hardened steel adaptor specifically to fit. However, the balancing guy has marked his modified adaptors for the next time I come in.