Try #1: Liquefied MDI adhesive.
For my first attempt I assembled hot water, a thermometer, glue, Diphenylmethane Diisocyanate (MDI) glue, and a straw. The MDI is a thick glue, so the trick was making it thin enough without creating toxic fumes:

- Used a straw to extend the tip of the glue bottle.
- Heated water to 120F to liquefy the glue in the bottle. Dropped knob in water to activate glue and heat metal.
- Turned glass knob to be as loose as possible, to allow glue to flow.
- Carefully poured glue inside, and "swished" it around.
- Dried the threads as best as I could.
- Turned glass knob to be as tight as possible to "clamp" the MDI glue.
MDI is an expanding glue, and indeed I had over-expansion which almost created a huge mess.
Also note the caution from customer service at Gorilla Glue:
Dear Bryce,
Heating Gorilla Glue before using it will thin it. The safest way to
do this is to put the bottle in a cup of hot water; do not boil bottle
on stove top or put into a microwave. If heated to approximately
120°F, the viscosity of the glue will be like water, and application
is very easy. Foaming is reduced a little. However, please note, that
the elevated temperature also increases the probability of releasing
MDI fumes, so this requires good ventilation.
Sincerely, Mary Ellen Customer Support Representative
The repair held but it was a fair amount of trouble.