Completely remove the Allen head bolt that runs all the way through the cooler. Stick a screw driver in the gap in the cooler housing (oil filter side) and evenly pry (down) around each corner and the cooler will separate.
Going straight up will hit the hangers and the thicker differential cover casing materials around the rear attachment points. Move the differential forward enough(towards front of car) that it clears the hangers and casing material and jack it up beyond the mounting points. While the...
Thrasher, shaft needs to go behind the rear tube it's touching in the picture. Remove the two bolts holding the shaft in place near the brake pedal and pull up and reroute the shaft between the tubes.