Would you admit that entropy might've played a role ?

Speaking of ACTUAL EVIDENCE, how do you explain the fact
that a 12.9 giga·year old black hole is a thousand times
more massive than the ones we see today ?

Unfortunately, the premise of your question is erroneous. The inferred mass of ULAS J1120+0641's black hole is large, but it is not larger than the black hole masses observed today. (ULAS J1120+0641's mass is about 2 billion solar masses, there are active galactic nuclei with estimated masses in the 10 billion solar mass range)

As discussed in this paper, http://arxiv.org/abs/1311.1686, the mass is unusual, and a bit of a challenge to explain, but there are reasonable explanations for these findings. When there are more than a ~million known quasars, there are bound to be a few extreme examples.

CM