The delay between the responses will be on the scale of minutes. Basically, I want to create an alarm that will go off X minutes after the intent handler is invoked. I don't need user input between the responses - perhaps there is a way to mimic the behavior of a native timer or alarm?
I think what you are really looking for is "push notifications". This isn't supported, but is the #1 feature request. You can go find the feature request thread and +1 it if you like. Personally I do not think Amazon will ever implement this due to privacy and legal reasons.
Agree w/ jjaquinta, and would add this to the reasons why it may never happen: look how horribly push notifications have been abused in app development, email, and even in terms of auto-play videos on web pages. It seems there are far more [b]abuse[/b] cases than [b]use[/b] cases for push notifications.