One brood box system — will this work?

You have to keep up with the balance of bees and swarming. Pulling frames in a timely manner to keep them to size without losing them to swarm. It is an interesting way of management.

OK, here is my two cents....right now the lower box or boxes are full of brood. As the Fall approaches the Queen will lay fewer and fewer eggs so the empty brood cells will be filled with honey, winter food. I would remove the honey supers (the beekeepers honey) in early September and force the bees to store honey in the empty cells of the brood boxes. Also remove Queen Excluders as well. You want the cluster, with queen to access the stored honey. It is necessary to start Winter with 120+ Lbs of honey for Winter food. Instead of one deep box I would recommend either two deeps or at least one deep and one medium for the Winter. Hopefully full of capped honey. I have watched the University of Guelph videos on Wintering with one deep. Not sure it is enough honey storage for our Winters. The main ingredient is to have plenty of honey available for them to eat during the Winter. You may need to feed sugar syrup in the Fall to help them build up a reserve.
The other main concern is the control of Varroa Mites. You can have a ton of honey stored in many boxes but if the mites are not controlled it is all for naught.
Good luck and by all means remove the Queen excluders for the Winter. Peter.
ps, next spring add a second hive for comparison sake. Maybe a split ?