--edit--

I tried cutting the "https:" and got my song to show the play controls-- and it froze. I then reloaded the page, and the controls no longer showed. Strangeness.

One more test (forgive the lack of hide tags)

Okay, after playing around, it seems the issue with the controls is either a browser or a Soundcloud issue or the way things in hide tags load/don't load, refresh/don't refresh (curse you, javascript!).  Sometimes, refreshing the browser let the controls show up.  Sometimes, adding or removing the "https://" part of the address made the controls show up.  But sometimes not.  

In 100% of cases (so far) though, not putting the soundcloud tags inside "hide" tags lets the player work fine with all controls showing. But because of the very large screen real estate of the current embed format, that might fill up too much of the page, especially if someone wants to share a few songs at one time. Maybe there's a paramater not to show the whole background and everything but just the functional player?

vBulletin has such a widget.