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
Given the diverse nature of OpenGL drivers, your best bet is probably to check the behavior of the major drivers (AMD / Intel / NVIDIA / MS Software Render) and on first startup run a test. E.g. if you can see that NVIDIA always slows down like you saw, then just run a quick loop till you see where the limit is on that machine (or rather, card). It's not much fun, but I think it's pretty hard to reliably push the limits otherwise.
In other words "best bet" is just like previously answered, you can't know beforehand.