Actually you might just be on to something. Having that special place for the day might help with the studying too if you set up your study area down there and make yourself be there so many hours per day doing your work and less distracted by everything else in the house.

Once the room is set up like an afterschool room instead of for mixed ages you should find it works better. It would be nice if you could change some of the solid walls such as to the bedrooms to half walls or put a cutout window in the wall for better supervision. You will be able to set up centres meaning each child should be able to find what they want to do and need less input from you in terms of playing and more just supervision. It also means activities will be spread out so instead of a small corner for the big kids you will have crafts in one area separate from lego from games from shuffleboard or whatever. It means stuff can be left out so lego for instance can be an ongoing but every changing layout. A mix of girls and boys will help to mellow things out a bit.

For your own baby, take one of the bedrooms in the basement and make it the toddler playroom with a gate at the door so you can control who goes in or out, put a chair in there for you to study from and that would work for a good portion of the day.

At night, as you say daycare closes and if you were able to get enough studying done during the day down there as you should have been able to do then you can close the door on that too and enjoy your family. Having the kitchen means you could also start supper if need be and just carry up when done - especially in the summer when you don't want to make the kitchen on the main floor hot.

I probably would plan on having the gang for PD, christmas, march but there are usually a lot of summer camp options parents could use. Depends a lot on what you want to do with your own school age because they will need entertained too so having a few friends might be worth it. I find over the summer with each family taking a two week vacation that I rarely have a full crew for July and August anyways which is nice and I plan according to the ages that will be here.