Did the upgrade, still no help.
The answer: We had put a second vmknic (1) on the hosts to support VXLAN. Rather than use DHCP, I manually assigned the IPs.
As it turned out, the IPs shared the first three octets with the original vmknic (0). Despite the fact that their subnet masks were supposed to be /25 and /26, both vmknics were misconfigured (by me) with /24 masks. Not good.
Once I put the appropriate /25 and /26 masks on the vmknics, things started working again.