I ended up using 2 tiny regular metal washers per screw and closing it back up. The washers prevent the fan from moving up and down but not side to side. The heat sink probably holds the fan in place well enough that I didn't even need the washers. Either way the replacement fan isn't quite as secure in there as the original. But the repair works -- for anyone else stuck at this step.

The original fan does not have removable rubber bushings. It has hard plastic ones attached to the fan itself. The original fan is a Foxconn PVB040A05H brushless fan.

Because I cannot remove the brushings but the guide assumes I can, the new fan cannot be screwed in securely, so my repair seems to be failing.