Sorry, I think you're SOL at the moment. The generic SVGA driver with Win 3.1x doesn't seem to be VESA compliant and of course, only supports a limited number of graphics cards.
Perhaps someone can get a copy of the Win 3.1 DDK and create a universal driver.
However, one last thing you COULD try is google around for VVESA - basically an old runtime driver for DOS designed for the old ATI Mach32 chips, though I can't guarantee it will work.