and probably worth it to a fair number of people.
That is absolutely insane.
That 11 1/2 hours is not in any way contiguous -- what could you accomplish in that time, in 114 seconds a day? How could that possibly offer any advantage, let alone one worth $35/hour?
Even if you could come up with some fantastic task that could justify the value placed on that tiny bit of time, who the hell can't manage to find 114 seconds of extra time per day? Go to bed 114 seconds later than normal, no weird untested toothbrush or dentist appointment required.
What if you shaved 19 seconds off the beginning and end of every meal? But I'm thinking too narrowly here. Just think how much time you could save by eliminating all those unnecessary trips to the toilet with a catheter!
You suggest that "fair number of people" would benefit. I'd love to know who these folks are, why their day is packed down to the second, and (most importantly) and why they're not all cathed.