On Android, pulling sliders from left to right bring out some type of index/menu drawer that obscures 90% of the screen, and I have to hit a narrow strip to dismiss it; if I miss that strip, I navigate away from the page.

It is quite difficult to do that on iOS since the "hit box" of the slider is rather small. You need to exactly hit the little point or it won't register (if you are used to iOS's native sliders, they are quite unsual).

Huh? The demo seems to be working fine on my iPhone. I'm using a 6s+ / current version of mobile safari.