Do you get a lunch hour?
Any chance of fitting in a quick lunch with friend then? Or a 40 min run and shower, to free time up elsewhere?
tbf, I work an 8 hr day, and commute for about an hr, so out of the house for 9-10h (depending on how much O/T I end up doing).
I have 2 small kids, and a DH who does lots of stuff in the house. Socialising comes quite a long way down the list!
Things that have worked are:
picking up kids, and going to a friend (with kids) house for a catchup, and tea. Kids into PJ's and teeth brushed at friends house, and into car to go to bed. Takes some organising tho, as I always take pudding with me (she can't visit me)
Single friend picks up take away on her home from work, and calls in after kids have gone to bed - we chat over dinner, and then she goes home.
I've also nearly complicated couch to 5k - its a hour max from work clothes to PJ's.
BUT, I don't have the study or the extended days! Hats of to you for fitting in the amount you do!