Take a carton box in which the glass fits easily. Wrap the outside of the glass with a thin layer of plastic (sandwich bag). Now, buy some gap filler (PU spray foam, aerosol) to fill the rest of the space. The PU foam has good filling and isolation properties. Once it is cured (24h), you can take out the glass and use it when necessary.
Please read the safely instructions on the label !! Good luck.
PS: the justification for buying the PU foam, lies in the that you already spent some time trying to reach your goal.
EDIT: background info:
It concerns polyurethane chemistry. Here in Europe this type of canistered foam is widely used on the building site. Its purpose is predominantly to fill cavities and act as an isolation material. It's made out of an isocyante (R-NCO) and a polyol (R-(OH)n) forming a urethane bond (R-C=O-O-N-H-R). Together with a propellant (hydrocarbons), it is pressed out of a canister. The left-over isocyantes will react with ambient water, to form poly-urea bonds. This embodies the curing mechanism.
The reason for me to suggest this particular product is because it fills easily and shapes any form. It will cure within a couple of hour. Quit often this material is chosen to prepare surprises (packages with surprises in them....)