So time in list power-up has some reports that I haven't explored, but it might be able to sum up all the time spent on cards in a certain label. (This screenshot shows the concept, but isn't exactly helpful to your case because of how i am using this board... it's for organizing my books, not for doing activities, so ignore the data, and just check out the format.)
Another idea... i was trying to do something like this before and i used a chrome extension called Scrum for Trello that basically sums up any numbers in brackets or parenthesis in a card title.
So i would add  to a card title to track how many hours i spent on it. Then you could filter the board to just show cards with that label and see a sum of all the hours spent in the Doing list.
This doesn't automatically track that time though, so I'm not sure if that solve the problem.
Lastly, you could also look at time trackers, like Harvest, they have Power-Ups that might be doing what you're looking for, although i imagine it would still involve you manually turning on a timer to track.
Do any of these help?
@WP - MARKETING Placker has list based time tracking, and I assume it will let you break this down by label (their gantt charting has a breakdown by label):
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