Just a little update for anyone interested in this; Yesterday I opened up my HHKB again and lubed the stems themselves, previously I had just lubed the slider rails.
The whistle is pretty much all gone. When typing it isn't there, but if I press 2 or 3 keys near the center of the board on the bottom row, which were the biggest offenders, you can still hear it, but quieter than before.
May be worth considering for anyone experiencing this problem.