Alright, here is the answer to my question:
Get a Rhino and store it in the Verdant Meadows garage. Once that is done, get a minigun and start the mission. Wait for the mission cutscenes to finish (although you can skip them to save the wait).
Once the cutscenes have finished, destroy the Andromada with the minigun. Then kill the secret agents, open the garage door, block it with the PCJ-600 (by parking it against the door), get into the Rhino and use it to push the Andromada into the garage. Once you have done so, waste yourself. You will fail the mission, and you will lose all of your weapons (unless you are dating Katie Zhan), however, if you are lucky, the Andromada will be stored in the garage and will be ready for you to pilot anytime.
New Question: Who is the Don of the Forelli Family during the events of GTA San Andreas?