Call the unit "Kilogram-Joules", abbreviate as KgJ and it works pretty damn well and unambiguously.
The problem is we don't live in a society powered by matter-antimatter annihilation reactions, or black evaporation so it's not really useful - unlike say, the electron-volt which at least serves physicists nicely.
428.6 kg relativistic mass-energy equivalent: https://www.wolframalpha.com/input?i=10.7PWh%2F%28c%5E2%29
But then, I am a silly person.