Freeglut runs on nvidia and is used in multithreaded applications. "Multithreaded" is not tied to the windowing api.
That said, i am not sure if the deprecated freeglut supports multiple opengl contexts if you want to go that way, but glfw for instance does. It also gives you much better control over the main loop.
I would also say, if a tool forces me to use a deprecated version of an api (here: GLUI and GLUT), i would not use it. There are enough alternatives that work without such dependencies. Also, if i understand it right, there still are unresolved problems and your code is a patchwork of versions. Wouldn't it make sense to first address these points on the checklist, before thinking about the user experience ? The later OpenGL Versions give you much better control about data, synchronization and all that. You don't have to craete new buffers every time data changes.