Not much statistical analysis in your post for a self proclaimed...

Not much statistical analysis in your post for a self proclaimed stats guy. Why not go through previous inclusions and compare the normalised performance post index inclusion over n years, then you could start to actually make an assessment of how unusual the BRN appreciation post index inclusion really is. To be fair I do agree with your overall point that inclusion in asx300 seems unlikely to be the only reason for the run up. Maybe something we don't know, the sudden difficulty in getting top 20 holders report is interesting.

On the other hand, the rise came after the slump driven by wider market forces, so the rise should be partially be viewed as a recovery from that. The CEO stepping down amicably is also something that would be driving speculation.

I think its also important to consider that a lot of people might have dismissed brainchip after last years blow up and consequently the market hasn't appreciated the Renesas deal and all the other irons in the fire. The same people will have started to think twice as they see brainchip creeping up towards the previous all time high. So there's a psychological barrier that I think is being slowly eroded.