This was already a one-day-old install of WindowBlinds 10.x
However, I created a new admin profile and uninstalled/re-installed WindowBlinds. I eliminated everything from the Startup section of msconfig and rebooted to the new profile.
I cannot duplicate the problem behavior in the new profile — but neither can I eliminate it by removing everything from Startup in my default profile.
I do see that the theme seems to be "stacking" tabs or subwindows (e.g., open mail messages in MS-Outlook) underneath the taskbar "button" for their application, but at a certain number of open applications, my pinned icons disappear behind very long buttons belonging to the running apps. So right now I have the window for Chrome and this page and a "button" for WinSCP — and those two take up the entire width of the taskbar, all the way to the system tray, despite MS-Outlook also running with one message open.