Hi Dooper,
After about a year of practicing the strike second deal (though, to be fair, not as much as other sleights) I still have a similar problem.
First, one little detail that might help you: Try resting the left thumb closer to the left upper edge instead of the right one. That might mitigate the sliding somewhat.
Apart from that little tip, I think it has to do a lot with your grip (which is influenced by your hand size), as in that some people have no problem holding the deck in a way that the bottom left corner still touches the palm at the correct point for the card to pivot like on a hinge. (That last sentence was way too long, if the meaning isn't clear, please ask.) My grip doesn't allow such a perfect hinge. So you'll have to work on what Josh Burch said above and actively "pull" the top card upwards with your left thumb when you feel it gliding downwards.
In the end it's down to practice. As I don't practice the strike second too much I still have this problem to an extent, but it's gotten much better than it was in the beginning. Don't invest in any more sources specifically on this sleight; what you've got so far is more than enough. Just focus on getting it down smoothly.
Another little tip: If you don't yet have some experience with false deals, go with the mechanic's grip (the first three pictures you posted). It allows you to do just about every false deal, looks relaxed and natural and doesn't have any major drawbacks. The full grip (all four fingers along the side of the deck) will present some major problems if you try to do a bottom deal.
I don't know if you already have some experience with false deals (if so, you can ignore this; you know what you're doing), but if you're just starting out I'd recommend you to practice with the mechanic's grip.
I hope this message will help you somewhat!