Recall that when Paul first started to play bass, using his guitar(!), they would cut strings out of pianos and use those. They might qualify as the original roundwounds.
Yes, I remember that story. And yes, I think that does qualify. I can't imagine that Paul would have purchased rounds on his own. So assuming the '66 Jazz arrived with flats, maybe Paul instructed Mal to cut the corresponding strings from the Steinway in studio 1. Hilarity ensues when, a few weeks later, Van Cliburn plays a low E on the Steinway but there is no sound. Same for the A, D, and G...