Does anyone know of a way to extract the plug that is fitted inside the boom arms just beyond where the tailpiece slides in?

plugs at both ends neb

Have done it. Get those fiberglass rods that hold up your 2-man dome tent and use them to push out the 2 plugs from the back-end of the boom arms (strong yet bendy)....after you have first unscrewed the head of course. Clean the pipes out with a chux covered in wd40 dragged through with a bit of cord. Put some a.c. tape around the plugs and re-insert. Waterproof!

I use a length of 10-12 mm dowel,
get a long chipboard screw cut off the thread
drill small hole and screw the blunt of the threaded bit into the end of the dowel about 25mm make sure its sniceantite
then use as a corkscrew pushing while screwing into the plug a few turns and pull it out.
to reuse silicone the hole and push it back in