While I am not disagreeing with you, I am sure you're aware of the common problem of using regressions on trending time series. The results are often spurious and don't necessarily indicate a causal relationship, as you mention yourself. More generally, the example of the BoJ would suggest that the expansion of the CB's balance sheet doesn't always and everywhere translate into higher equity prices. For instance, between 2000 and 2005 BoJ's balance sheet nearly doubled while Nikkei was roughly unchanged.
I am very curious about the other data points you're referring to. Again, I am not disagreeing, just interested in the argument.