Not quite the same, but I've just had my 5th surviving child. Although DC1 no longer lives at home, I usually have a 12 year old, a 9 year old with Downs Syndrome and a two year old at home, plus the new baby. My DH is in the army, so we have no family near and he works long hours/is away a lot. We also have 3 dogs, a cat and four rabbits.
I only managed to successfully BF my none 2 year old, who finished a few months ago, so I've FF too. I am BF the baby and wouldn't have considered anything else. DH went away for a week and was uncontactable last week when our newborn was a week old.
It just means being fairly organised, realising sometimes other things will have to wait a bit or most of the day (children's dinner maybe the prior, housework the latter) but I don't think that would really be much different if I was bottle feeding a newborn. I have a sling which I use if we go out and around the house so I can get things done. I've got a slow cooker to do meals if I need to, a few filling soups in the freezer I can do for dinner and I have to admit, I've resorted to using easier things that can just go in the oven for a bit like chips, fish fingers etc which we don't normally eat.
The house is quite child proof downstairs so I don't often have to leap up to rescue the DC...
I bedshare with the baby for maximum sleep. I do though, hold the baby pretty much all the time, although I have a swing in the kitchen so I can pop him in there while I get breakfast, load the dishwasher, cook dinner etc if I need to.
I can't imagine bottle feeding now tbh, it seems such a huge faff.