The Avensis has a huge boot, especially with the seats down, I'm assuming its a hatchback & not a saloon? I once fitted an engine & gearbox for a Subaru Legacy into the boot of an Avensis so I would say it will probably fit.
Got an Ml10 and original stand in the back of a mondeo hatch back. Seats were not down it was swallowed in the boot no issues. It's a bit smaller than a 7 but with the seats down I'm sure there would be no issues making it go in. Look on Myford web site for dimensions then go out to the motor with a tape to be sure.