To make the applicator, I unscrewed the cap and pulled the brush applicator out of the handle. It easily pops out, making it easier to modify. Basically, I used an ExactO blade to cut off the bottom end of the brush, then trim the end into a taper to fit inside the tube.
Set the modified applicator in the bottle, then screw the cap back on, which will reseat the applicator into the handle.
You now have a solid applicator with a very fine end, with a hollow inner section. The fine tip and solid construction should make it easier and hopefully more precise method of applying head cement.