The HTC is the opposite of the cryogenic freezer or relativistic chamber - it accelerates time for people inside it, allowing you to meet external deadlines while the world passes by slowly outside. A cryo freezer or relativistic spaceship decelerates time for people inside, allowing external activities to be accomplished while you don't age.
You are right, I'm wrong. I thought he had something in there for that anyway, but apparently not. Still, you're just on the other side of the Amdahl’s law problems, so you better hope no one is depending on you.