How to factory reset a MacBook Pro 2011 with a messed up GPU
There are apparently quite some options left now.


Boot into SafeMode. Hold shift key on StartUp
You will get unaccelerated display but the drivers for the GPU are not loaded and you should have still full access to the disk. Delete to your heart's content.
Take out the drive and mount it into an external case. Attach it to another Mac and do with it what you like to do.
Circumvent the discrete GPU by using this procedure This will give you an internal dsiplay with graphics acceleration from the Intel GPU. Remove all the stuff you like in that now resurrected MacBook Pro.
Create a USB-installer and boot from that thing. The installer should not use the discrete GPU and gives you the option to wipe/format the drive. That would be the true "factory reset".