All Sony Xperia Z experts,
No changes on the situation.
Overall, I am quite surprised how little reaction this issue has caused with you guys. This is an unlocked BL, rooted phone with a deodexed 10.3.1.A.2.67 firmware. So, rather standard. I use the stamina mode, causing almost no battery drain while idle. The phone never dropped battery below 30%. I am not using any apps to mod CPU or other fancy settings. This significant issue could happen to many Sony users.
I will contact Sony to see what they can do (not much I guess). In the meantime, if anyone else experienced this problem, please contact me.