I wouldn't bother attempting to bypass the steering lock anymore after damaging the key cylinder. Since the steering lock is a mechanical component of the ignition/column assembly on a 2001 Camry, a broken cylinder would cause the wheel to remain locked even though the steering-lock mechanism is still in use.
The steering lock is an anti-theft mechanism, so I will not show you how to defeat it. However, there are significantly simpler solutions for your primary objective, which is to move the vehicle a short distance within your own property without a key:
Set up wheel skates or dollies beneath the front wheels. Since the 2001 Camry has front-wheel drive, shifting into neutral and then positioning the front tires on suitable automotive dollies enables you to move it without steering.
Use four wheel dollies—one under each tire—to free the rear wheels that have been sitting for six years.
A tow truck service that has a flatbed or self-loading wheel-lift can move it in a matter of minutes without needing a key.
Additionally, a mobile automotive locksmith can evaluate the broken ignition; however, they will typically require proof of authorisation to work on the vehicle, as it is owned by someone else.
Instead of sloppy, inexpensive furniture dollies, I would use rated hydraulic wheel dollies for a brief move across the yard or driveway. To level the vehicle, you simply lift it off its wheels using jacks, lower it onto the dolly, shift into neutral, let go of the parking brake, and roll it. Use wheel chocks to maintain a level surface and steady the vehicle until you are ready to move it.
Additionally, put the screwdriver out of its ignition mode. Changing the steering column becomes a relatively easy locksmith or ignition cylinder job if the lock housing gets damaged.