The broom worked for me on an f2 , but I cut the handle down so it rested on the naughty bottom tube, and was just long enough to get the top fork bolt in a few turns to put some pressure on the tube.
If you try this, tidy up the sawn end of the broomhandle so you dont leave splinters or other debris in there. ooh, and hide the rest of the broom from mum/wife/sister/janitor, and practice "knowing nothing about that" for when its found...