Hi @tom! Welcome to the Community 
I think you and @ashacklett have a similar request if I understand correctly:
Delays cannot be passed on to Apilio currently as you describe, but my first work-around solution idea would be to have 2 or 3 of logicblocks that can be launched from IFTTT with a do-button from the app, or maybe a voice command, each one of them with a different delay: maybe 5 minutes, 10 minutes, 15 minutes? And then you run the specific Logicblock depending on the time you need.
What do you think? Thanks!