Until now...
This part of the Strat tremolo is often overlooked during the preparation process. These threads need to be lubricated and cleaned quite often, as the beep hole in the trem block is the perfect place for grime to hide.
Many players use a graphite lubricant for many areas of the guitar, but for this particular spot I recommend just a drop of clear mineral oil on the bottom few threads. Graphite lube in this area will only accumulate more grime over time.
With this guitar, the bar has broken off rather deep ~ below the surface of the trem block if it were to be removed. In cases where they break off flush or slightly below the saddle plate, removal of the trem block would allow you to unscrew the broken piece by hand as it would be exposed above it's surface ~ no drilling required.
Despite centre punching the piece, these extractions can often go awry due to the uneven surface created from the break. After a visit to the drill press, the hole meandered off centre but I caught it on time before it damaged the threads of the trem block. Just enough of a hole to use the extractor bit to remove the piece.
I noticed the piece was quite short, meaning not a lot of thread was turning in to the trem block. When I attempted to install a new arm, the threads were very stiff and it was obvious they needed a good cleaning.
A liberal amount of mineral oil on the threads of the new arm, and working it back & forth in the threads began to work the grime lose. The threads were so tight with buildup that the arm could only be threaded in half way before it was tight, which explains why the old arm broke off so short.
Each time the new arm was threaded in tightly, it was removed, cleaned, re-lubricated and threaded in again going further every turn.
It didn't take long to feel the results ~ the new trem arm threaded in all the way down with the appropriate amount of tension.