I was using MatLog app, it has the Record to file option, though I am not yet sure if that would do the trick. Like, what if the file won't get updated because the phone froze? Tried to test it but no luck (ironically) so far.
Also had freezes exactly like you've described it. The phone either does this, or completely locks up and won't light up the screen.There, I had the freeze again. I have the time but I was not recording logs (any recommended logcat app?).
Power button was responsive,the screen was frozen at a certain time an hour and a half ago and most importantly the top notification bar was double, as if it were another one superimposed.
When long pressing the power button, I felt the haptic feedback of the power menu so it was there but the display was hung.