I do something similar without the math - a habit from my days flying to/from California.
- Sent to a new Frequency - Stop the Clock
- Check In - Start the Clock
- If I see 20 minutes I start thinking about the Controller stranding us.
- If (more likely When) I see the clock not running, I know I've been sent over but not checked in. I try to wait a bit after changing the frequency to avoid stepping on someone or interrupting a request.
It's anal, but it's helped me maintain situational awareness more than once.
On Another Note - how many of you read back the actual frequency to the controller before changing? I don't domestically since it's easier for me to remember it without reading it back (go figure). I do ask the Captain if he has a preference; he usually says "Nah, don't worry about it until you mess it up."