My .Net Winforms application creates three OpenGL rendering contexts in my main window, and then allows the user to popup other windows where each window has two more render
If you go through that much trouble to set OpenGL up in a over-the-top multi-threaded fashion, you could as well benefit from it and consider switching to Vulkan. See, by design, the OpenGL architecture funnels all the hard earned context/thread separated drawing operations into one single driver thread that then redistributes all these calls acrosss virtual hardware threads that map onto each context. The driver is in essence a huge bottleneck because it is not itself threaded, despite any glewmx sitting aroung. It is simply not designed to handle this well.
That said, I am curious if you used an older version of Glew, or if you do all the extension handling in some other way, since latest glew libs no longer support mx. One more reason to switch.