Hypertime and the Electric Plants

In a lot of media, there's places where time flows at a different rate than normal. The amount of time in and the amount of time out don't match. The closest real equivalent to this is special relativity time dilation, and that usually works in the opposite way. (The person accelerating experiences less time than everyone else.)
Anyway, this got me thinking about the movie "Clockstoppers" and their central mcGuffin, the "Hypertime". In the movie, the protagonist's scientist father invented a device that shifted him into a paralell time axis, ("Hypertime"), in which one could do time-like things and yet no time would have passed. After a long sequence of teenage boy antics and showing off for a girlfriend, the device is stolen by the movie's villain to set the center stage for the plot. And this gave me ideas.
I'd sleep in hypertime. I'd arrange for a hypertime room at work, and breaks there. When some problem has be absolutely screaming in irritation, I'd punch out, go to the hypertime room, take an eight hour nap under sedation, goof off for another four, and then return to work as no objective time had actually passed. I'd write this blog in hypertime and have two or three posts a day. Except, nags the nerdy part of me, some of this is just plain implausible.
No time means no outside electricity and no airflow. I'd suffocate while asleep. While there are existing solutions to this, such as chemical rebreathers (they have caustic solutions that absorb the carbon from your breath), my mind was already at work for alternatives, which could be useful in the real world.
The electric plant would, given electricity, strip carbon off of carbon dioxide, thus keeping air breathable in sealed environments. And provide a large source of carbon powder, which can later be sold as fuel, recovering some of the cost of the electricity. Extra bonus in solar-heavy rural areas like eastern California and Arizona, where you could have entire ranches of solar panels plus electric plants, sucking the carbon out of the air and gathering it for sale. Both to the coal plant to burn as fuel and to the pencil factory to stuff into pencils.
Portable power systems are a little more practical. Car battery, basically, that would be charged in a time environment.