The Tower
The test is not complete. Checking only 20 of the 24 variants, I easily pass all the tests. Here are the sides I verified (side-by-side recordings):
[ '1243', '1342', '1546', '2134', '2431', '2536', '2635', '3124', '3421', '3526', '3625', '4213', '4312', '4615', '5263', '5362', '5461', '6154', '6253', '6352' ]
As I understand it is the case when the cube turns 90 counterclockwise. But I just can not think up examples to close this gap.