So... I ended up making my own homemade USB A-to-A cable. I simply cut
two old cables in half and spliced together the wires. This cable
works perfectly fine with this hard drive enclosure. I was actually a
bit surprised that it can do high-speed USB over this cable with no
problems, considering that the spec requires a TWISTED pair of signal
wires. I guess the length of wire that I mangled is only a few cm...

Dan