Courtman - your method is doomed to inaccuracy because you are not equating the correct proportion of an hour to the corect decimal. If you use 6 minute increments, every 6 minutes is 0.1 of an hour. If 6 minutes is too large an increment for your purposes, every 3 minutes is 0.05 of an hour. So you are likely, by rounding up or down to the nearest 0.05 to be much more accurate than the method you are using at present.
If periodically, you then need to convert the deimal recording to hours and minutes, of course the hours will be accurate anyway, and you simply multiple whatever aggregate fraction of an hour you happen to have, by 60, in order to record the correct number of logged minutes.