At the end of the day, it’s key to find the right kind of balance for everything that’s going on in your life. The batch work idea you have is a great move and it’s something that I often do on Thursdays. I find myself going someplace relaxing and working for several hours. I tend to get a little over 1000 words per hour for four hours.
It might not be fitting for you at the moment, but I think finding a nice quiet place to work outside of the house could be good and could be incorporated in your life at various points. Good luck out there!