Now shortly after that 5 day streak of very bad luck, the luck suddenly shot up to 70% for a day! I found that kind of odd.
I think questions should always be asked, so I don't begrudge you for putting forth the notion that BTC might be cheating.
However, people are notoriously poor judges of randomness. The "hot hand" in basketball is a classic example that statisticians use of sports fans attributing skill to what can be explained by a good run of randomness.
As you said, the luck suddenly shot up 70% for a day. Rather than focusing on the five days, it might make more sense to take an entire month, which includes the one good day and all the bad days. Put another way, I'm sure you know that flipping a coin and coming up with five heads proves nothing, even though the probability is 3%, which in the parlance of this post implies a 97% chance of cheating.
As a final note, your calculated probability of 0.6952% (which I have not verified) is well within a 4-sigma event (0.0165%). Four standard deviations is hardly considered extreme.