You don't need the API for this, just JavaScript/jQuery and the script that's included in the JavaScript (Website) embed code: <script language="JavaScript" type="text/javascript" src="//admin.brightcove.com/js/BrightcoveExperiences.js"></scriptGGT
You need to remove the current player from the DOM and inject the new one - easiest way would be to wrap the player in a div and then set its HTML to the player code. (Simply replacing the player ID and Key after the player has been instantiated won't do it.)
Then you need to call
brightcove.createExperiences();
Also, see this article