Hey Martin
I know a few people that have to squat narrow because of issues in the hip. But they mitigate this by turning the toes outward more.
You really need to get a hold of some lifting shoes if you can.
In both videos you're not leaning over enough and trying to stay too upright.
The lumbar wiggle that you're seeing as you hit the bottom is because you're over-extending the lumbar spine to start (while trying to keep the chest upright) it's getting to a more neutral position. The position it should start and stay in. If you have any money left over after buying some lifting shoes, immediately buy a belt.
You're one of the few unfortunate folks that is going to have to modify the squat further from the model, but it doesn't mean it can't be done.
Buy some shoes, turn out the toes more, get the back neutral and tight, lean over more to keep your center of mass over its center of balance, stay midfoot throughout the movement, buy some shoes.
See if that helps.