The mechanics who work on my car can not determine the exact cause of the problem and are unwilling to gamble - that leaves me basically on my own. Because I really like the car (its a nice one) I am willing to try logical options...particularly if the things I'm replacing are old and due for updates anyway (rationalizaing here).
I have read several comments about the axles that indicate they could be the culprets. You suggest that in your post. Cost will be about $300 per side using rebuilds. I can stand that. I wouldn't mind trying the switch'm idea but my labor cost would be $200 for that experiment (I don't do this work).
If this doesn't solve it I'm out of options. I just hate to give up.