You ought to have four options to choose from for after-alarm activities: nightmode on, nightmode off, power off, and nothing. Unfortunately, it's not possible to switch channels through such an interface, mostly because I couldn't find a way to get a listing of available channels, with IDs. Just like it's not possible to come up with the arguments to an audio source through the web, because it requires information that only the Control Panel can know.
It is, however, possible to create alarms through the web and set their name and frequency, and then go back through on the Chumby and set up the audio to play and the channel to switch to.
One of the reasons I created it the way I did, namely entirely in perl, is because I wanted it to be hackable. Everything from the CGI manipulation to the file parsing is done in pure perl, enclosed within two files. As Duane pointed out to me, this could easily be extended to handle editing My Streams. If someone wants to extend this to work on editing that, I encourage them to do so. Or, really, anything else.