If you could do that, wouldn't you be able to just use the Recovery Partition?
No, because the recovery on the tablet's memory seems to be corrupted (Problem with no text mentioned in OP)
The recovery I would be using would be one that Windows 8.1 installers have, not the one on board.
You probably know that at the beginning of a Win installation there's a "Repair your computer" button on the lower left corner, that's the recovery I'm thinking of.
Any Windows 8.1 install you have won't accept the PID Win8.1 w/Bing.
You would need the Win8.1 w/Bing install which is only available to manufacturers.
I found Win8.1 with Bing images on *cough*that one torrent site*cough* but I don't know if it's illegal to use them.
The plan was to download that disc image and to install it using the
legitimate key I recovered, how does that sound?