It would need to be the other way around, dark energy being matter falling into our black hole. Hawking radiation should 'suck' energy out of our universe. I can't think of a satisfying source of this energy.
The best I can imagine is either space contracting (but that is gravity) or entropy increasing (but that doesn't leak energy, just free energy).
Something to consider is a possible time scale difference. Eg time could be dilated for us for being around so much density.