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Another approach you might consider is:

  - 4 to 6 hours of dedicated/uninterrupted work per day
  - 6 to 7 days per week
  - Wake early, say 05:30, and start work right off the bat

I looked at my own GitHub work history to see when I was most productive and also read a book about how many of the most profound creatives worked in their own lives. Both suggested such a structure and it allows/addresses many of your concerns (i.e. I also have a child, need to do chores, don't want to count hours but productivity, etc). The thought being many work best early in the day, you only have so many hours in a day you can focus on hard problems without wasting time, and consistency is a virtue.