Here's my suggestion: have your users create individual SoundCloud accounts for themselves, then create an interface that allows them to share individual tracks with you, which you can then aggregate into a playlist of some sort (which could then be streamed to whatever device you wish, via SoundCloud).
This has the following advantages:
- You maintain control of your own personal SoundCloud account and don't have to worry about it expanding to an unmanageable size.
- You have the ability to moderate tracks, allowing you to screen for copyrighted or troll content.
- It's more extensible -- if you use something like Drupal's aggregate facility, or a plugin like FeedWordPress (not sure what your CMS platform is, if any), the RSS feeds of tracks you're using can also be taken and used elsewhere by your users, thus potentially increasing the size of your audience. I.e., a widget that displays the latest tracks people can drop onto social profiles or blogs or whatever.
- If set up well enough, your solution might be able to encompass non-SoundCloud streaming sources -- YouTube, etc.
Basically, you're dumping links sent to you into an RSS feed, which are super easy to work with both cross-browser and cross-OS. I'd personally use Drupal for this, but I'm sure there are ways to do this just as easily in Joomla!, WordPress or any other CMS worth its salt.