Just an update, I did test 17728.1000 last weekend, but not for very long. I couldn't make the second issue (notification overflow window getting cut off by the taskbar) happen. However, last night I installed 17735.1000, which was just released a few days ago. I tested with that today and, sadly, the second issue is apparently not fixed:
That Uplay icon is getting cut off.
Sigh, I'm going to report this to Jason on Monday.
Update: I've been testing this more over the weekend with more notification apps installed, and the issue does seem to be improved, as the only app icon having problems is Uplay, and it sometimes completely disappears even when running (and showing up when making it always present on the taskbar).