Create a "dummy sector" (a sector off to the side, outside the thok barrier, that cannot be reached without a "no clip" code activated). Set the ceiling to what you want the floor of the FOF to be, and the ceiling's texture to what the floor's texture should be. Set the floor to what you want the ceiling of the FOF to be, and texture that too. Set the dummy sector's lighting to that desired for the area underneath the FOF.
Once all that is done, right click any of the lindefs (sides) on the sector. Set its property to whatever the FOF property is you want (likely 25, the plain vanilla one with a shadow). Set its Middle texture to that which the FOF will have on its sides. Set the tag to an unused number.
Now, inside the thok barrier, create a new sector for the area to have the FOF. Set the sector's tag to that of the lindef. If all goes according to plan, there should now be a floating block where that new sector is, with the height of the dummy sector and all the textures as previously mentioned.