Yes, the tests run in the video as well as your tests have convinced me that the phenomenon is a real one. Those efforts, as well as those of the OP to bring the issue to light in the first place are definitely a contribution and it is an interesting.
Comments after the video also suggest decapping as, potentially, a definitive test.
I don't want anyone, especially me, to spend any money decapping chips. But I think it's worth trying to get a response from Microchip. I'm hoping Kevin Darrah can do that. He mentioned in email trying to contact an FAE he's talked to before. Field Applications Engineer? That's probably not the right guy to answer the question, but maybe he could refer Kevin to someone. In the end, whether they are counterfeits or a bad run or whatever, I think we're all going to have to be careful about any clone we buy that uses a 328P which (so far) is dated in the last half of 2019 and which has a fab code of TW or KR. So far nobody has mentioned having a chip with those markings that actually works properly. And of course we don't know if sleep current is the only issue with those chips.
My original problem was that after two tries with two different sellers, none of the Pro Mini clones I received slept soundly. But at least we know now that Microchip's current production is good, so in the worst case I could buy genuine chips from Digikey and try to find someone locally to switch them out for me.
I would hope (with more of a sense that it would be nice if things worked that way, than any evidence) that some other characteristics of the "bad" chips would be found to be different - something like NOT turning off a peripheral, as being responsible.
Yes, that's what I've been hoping for. If there's a software fix - some bit in some register - then no harm, no foul. I just don't know what peripheral consumes 150uA at 3.3V. I know it's not ADC or BOD because I can measure those as using the same current on both good and bad chips. But I don't know for sure about WDT. In my test sketch I turn it off, but Kevin doesn't bother, I think because the Arduino bootloaders all turn it off by default. But turning it off in the sketch, or not, has no effect on current, so I've assumed it was already off, as does Kevin. But thinking about it, it might be worth changing the fuse setting so that WDT is always on. If that raises the sleep current on a good chip to, say, 150uA, but has no effect on a bad chip, that would be very interesting. But otherwise, I just don't know what other peripheral could have been left on.
On the other hand, it seems like there is a specific time niche that these "bad" chips were made, based on some markings - no?
Why would it be happening with only that package of the 328P (at least so far)? Why not the DIP package, for example? Is there a reasonable explanation for that?
Well, we may have an example of a bad DIP package. See Ralph Bacon's video on using the DS3231 to wake up an Arduino. He puts the 328P-PU to sleep, then manually disconnects power from the DS3231, and ends up with a sleep current of 150uA. He blames that on the I2C lines, but he has disconnected the power to the module, so I don't see how that could be the explanation. I've written to him asking for the markings, and asking him to try again with an older chip to see if the current changes, but have not heard back from him, and it's been a while.