I'm confused as to where the heat from the radiator is being blow. Straight up through the case or is there some grating on the bottom of the case it is being blown through?
Most midrange and higher cases now days have vent grill at the bottom of the case sized for 120x240 or 120x360 radiators for large water loops. The PSU usually covers up some of that vent. So to answer your question; the heat is blowing down under the case which probably has an inch of clearance due to base pegs. If your case does not have this feature, you can fairly easily DIY if you have a dremel or something similar.
Heres a few examples of modern style undercarriage vents.
The pictures of the GPU mods I posted only show a few possible mounting configurations. Some use the front HDD drive bay fan slots. Some double sandwich with the CPU radiator at the CPU exhaust slot. Some use brackets to hold the fan and rad outside the case, attached to the back near the expansion slots like many old school water cooled configs did in the past. Although it is probably a bad idea, you could also use the side fan slot. The second config shown in the pic has the cpu rad exhausting up top slot, with the gpu rad exhausting rear at the cpu exhaust slot.