If your carefull you can just slacken off the side screws at the top/side, even take some out, the wood is flexable. This will allow you to make enough space to get the rods out using the open corners.
Getting them back in is a bit harder with the pillows attached.
The cogs on the rod ends can be tapped off.

My rods were slightly bent at the ends due to shipping/usage... so check this by rolling the rods on a flat surface.

Once in place, mark the holes with a sharp point, drill and screw them in.

The front face pillows needed an extra 2mm of standoff, I used washers.

Good luck.