Found it – Peter Velichkov has a link on his blog. After updating to kernel 188.8.131.52 (which worked fine), I ran the script (runme.pl) and fired up VMware Server. It seemed to work fine, with no real issues, even after rebooting the VM, other than being a little sluggish, however.
To fix this, I reinstalled the vmware tools (VM menu, Install VMware Tools) – this has to be done while the Windows VM is running. After a little churning, the VM presented me with three choices – I chose to Repair. This required a reboot of the VM, but I noticed an immediate improvement in the VM’s performance. Not sure if it was because I updated VMware tools after going to the update116 patch, or if it was due to VMware having stuff buffered in memory, but I will bet on the side of the tools repair.