[YouTube-API] Javascript API + iframe embeds + iPad not working?

I have a page with youtube videos embedding via the iFrame API. For
each video, I've made a fancy "Play" button that, on click, fires
playVideo() from the Javascript API.

In desktop browsers, this works great.

On iPad, the videos embed, but if I hit my "Play" buttons, the video
appears to begin loading (the thumbnail disappears, is replaced by a
black box with a spinning load icon), and stays in that state
perpetually. No video ever appears.

However, if I click directly on the video, and bypass my fancy play
button, the video begins playing as I would expect it to.

So, I would assume that this is some disconnect between the js API and
the video, only on iPad. I've confirmed that the onReady state is
reached for each video.

I'm wondering if this is a bug, if I'm missing something, or if
there's a way to work around this? Unfortunately, my current project
requires the "Play" buttons, so just doing away with them doesn't seem
to be a good option.

Thanks in advance for any help.

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