Lets see. Transmission holds 14quarts. Do a complete flush and you'd want to have a couple spare quarts just to be sure you got all the other stuff out, so theres 16 or so quarts. Just a tick over three gallons. Service time comes up you can just drop the pan to buy some time until you can flush it again, that holds about 6 - 7 quarts. So yeah, I could do a 5-Gallon bucket.
I cant imagine what shipping would be, but with your proven track record I could go for it.