This is a good project, you will get some good experience. Years ago before electronics this is how most clocks in buildings were synchronized. You can check how they did it and you do not have to go in reverse, stop at 12 until you get the pulse, if you get the pulse early step forward to 12. There are a lot of clock tutorials on line and many alarm clock ones as well. With the alarm just set the alarm at 12 and when it trips sync you clocks. In many current commercial systems a synchronized clock system, the master clock receives time from either an NTP server or GPS receiver, or its internal clock can be utilized as a time source. When the master clock has received the correct time from either source, the time is then distributed to all slave clocks in the system. Try searching for "sync time clocks 1950" you will find a wealth of information.
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