I’ve replaced all instances of the Flash-based SoundCloud audio player on this site with the HTML5 version. Fortunately I didn’t have hundreds of widgets in posts, but only about 18 so I just manually updated the code. There is a workaround for bigger migrations on WordPress sites here.
The new SoundCloud widget works well with all devices including mobile and its design follows open standards allowing for faster development. Its looks need some finishing, and currently there are few options for customisability, but it is good anyway, a stable and efficient little gadget.
I didn’t know the widgets I was using were invisible on some devices until my friend said they were missing when he viewed the site on his iPad. Thanks for the helpful feedback Hoonose!