I updated the spreadsheet. I did the test with the MP3 player again, this time fresh battery without Battery until it was dead, then waiting for 2 days, like for the Batteroo test, but using this battery again without the Batteroo sleeve. Extra time was 71 minutes, compared to 109 minutes with Batteroo. So Batteroo has a little bit of use for this device, maybe because of the high cutout voltage of 1.1 V. Dave's MP3 player extra time was 30 minutes and 45 minutes with Batteroo, and cutout voltage 0.9 V. Of course, doesn't matter much if you compare this with the 10 times higher initial time with a fresh battery, still far away from the 8x claim. And the drastically reduced time if you use Batteroo from the beginning with a fresh battery doesn't help either.
And I added the tests from Ysjoelfir: more than 8 hours without Batteroo, multiple tests with Batteroo, where the light bulbs lasted between 60 and 90 minutes until they were destroyed.