What to do about a broken rear derailleur inner cage plate?
The relevant document is Shimano EV-RD-6800-3608A (Jun.-2013-3608A), which gives an exploded view and part numbers for each of the parts of the derailleur. For the Shimano Ultegra RD-6800 SS, you're looking for Shimano Y5XH08000 for the inner plate. (This also applies to many of Shimano's other parts to find replacement pieces)

Given that you've invested in Ultegra level gear, I'd not risk it and just wait for the replacement to arrive.