Did you solve this. I still think wire would be easy to use.
It doesn't have to be very thick: something like fuse wire would do or something like gardening wire.
You could put the screws directly into the HHD and put the wire round the screw to secure it like you would on any sort of screw electrical connection. The other end would go through a hole in the sled.
They you could twist them in an X across the top, snip it off short and push it flat.
There must be something simple like that possible to do.