After picking up the invulnerability sphere, I experience some major slowdown, followed by some sort of graphics driver exception/crash. I can repeatedly trigger the slowdown/crash by warping to map08, entering the door with all the barons and single cyberdemon, and then picking up the invulnerability sphere.
Go into Menu -> Options -> Video Options -> Invulnerability Method. What is this set to?
Try setting to Simple or Textured (the default is Complex).
Last edit: Corbin 2015-08-24
INVUL_FX (COMPLEX) was causing problems with the engine's handling of backface culling for 3D models. Instead of trying to fix this problem, I have eliminated the COMPLEX option from the Video Options (now, there is only Simple or Textured).
This has been fixed with version 2.0.2 (released August 31, 2015).