One can have the same issue with a Langstroth hive: the usual solution is a queen excluder (or several frames already full of capped honey) between the brood box and the honey supers.
One can place a queen excluder as a divider in a Top Bar hive much like one can do so with a Langstroth style hive. The shape is different due to the sloped sides of the top bar hive, but the approach is the same.
Similarly, one can run two-queen hives in a Top Bar hive: a colony on each end, two queen excluders, and a communal honey section in the middle. Until the hives are strong there may be some unused space in the Top Bar hive, so one would need to handle that through either placing the colonies closer together, or by inserting some space-filling boxes to mask off certain areas of the hive until the colonies grow strong enough. This is the TBH’s weakness, though: one cannot add additional supers easily to a TBH. Instead, one must keep up with the honey produced and extract on the bees’ schedule in order to make more room (but too much honey’s a good problem to have).
Re: honey extraction
Top Bar hive owners usually use the scrape, shred, and strain method of honey collection. Not the most efficient, but TBH’s are not really for large scale production. Someone using TBH’s likely also won’t own a cappings knife, radial extractor, honey heating tank, etc. I was never concerned with the quantity of honey I produced: I used Langstroth hives and the scrape and strain method with a strainer made from 2 five gallon pickle buckets and some fine-gauge netting. Made for clear, tasty honey, albeit slowly. I fed the honey-soaked cappings back to the bees rather than trying to separate the remaining honey from the cappings via melting (again, not using a commercial operation’s goals).
I kept multiple hives of bees for over 20 years (gave them up three years ago) and have mentored a few people in getting started in beekeeping. It’s a great hobby.
I recommend that newcomers to the hobby plan to get at least TWO hives to start: that gives you a 2nd hive to compare a hive’s strength, and gives you many disaster recovery options a single hive won’t support (e.g. swapping hive locations to balance worker bee populations, swapping frames to bolster a weak hive, combining hives if a colony loses its queen, et al).
In the DFW metroplex, I also strongly recommend the Collin County Hobby Beekeepers Association: they are a strong group (or were when I was attending), have monthly “bee talks” on where your hives should be, have a wonderful mentoring program for teen beekeepers from non-beekeeping families, etc.
Their 2nd Monday monthly meetings are at 6:30pm at the Collin College Conference Center (Central Park Campus), 2400 Community Ave. in McKinney. The next meeting is in three days: Monday, 10 Feb 2020.