Have the wheels actually been balanced by someone who knows how to balance wire wheels? May seem a silly question but I had persistent wheel shake and had the balance checked in UK and France by ordinary tyre companies, made no difference, thought of flat spots as the car had stood for several months unsupported. Spoke to Bob at BHM who checked the wheels and found that the balance was better with all the weights removed!! He then rebalanced the wheels and now no problem.
Just a thought from an amateur.

Andrew