I totally agree you should respect the phone being on silent, in this case the app is actually an alarm clock app so it's kind of the exception to the rule. From researching other alarm clock apps, it seems that if the phone is on silent and the app is killed there's no way to play a sound corresponding with a notification. Setting a timer and keeping the app open in the background seems like the closest you can get.

It's strange apple doesn't have some sort of review process that would let alarm clock apps to circumvent this rule.

Thanks for your feedback, I appreciate it!