You won't have to enter your schedule - there's APIs for Calendars. You'd just have to determine which calendars are considered "busy".
As for upkeep, I found that the app is self-motivating. It's not measuring anything so if you miss an hour or a month it doesn't matter, there's no overwhelming guilt. The only thing you miss is being able to review what you worked on.
not trying to be negative about your idea. but the best app is one that will know automatically what's on my schedule, without me having to enter it explicitly. that way I can't forget. I have no idea how to do this, it doesn't really sound possible. Just trying to convey my experience with projects like you described