I think you're confusing adaptor refresh rate with game speed. Using a higher refresh rate will give you a nicer image, but won't affect Quake in the slightest. As the Picasso doesn't have any 3D acceleration, Quake is running in software mode, which is really slow on a 68060. On the 68060 50Mhz, in order to complete ClickBOOM quake I used 2x2 pixel mode, and a small window, in 320x200.
Asking a 68060 to do Quake at 640x480, without the help of a CVPPC or Voodoo 3 is just too much.