I am zone 5a, but I use strawberries as a groundcover, and they have been fantastic. The everbearing kind keeps going from June through to November! They make a very effective groundcover and have been my breakfast, mixed with cottage cheese, almost every day since June and we are headed into March as I write this.
I would also suggest that you may want to plant some asparagus...obviously, it's not a berry, but I planted 50 crowns about four years ago, and while you have to be patient the first couple of years, you will have enough to be eating your fill in very short order. You could plant much less than that and still have a ton. (I want to have enough so that I can bring the extra to the food shelf.) You can then pickle, can, freeze-dry, whatever. When it ferns out, it makes a pretty backdrop, almost like grasses, and provides a sense of privacy. I planted the crowns behind my Regent serviceberries, which only grow to 4-6 feet. The serviceberries are a beautiful berry because they go from pink to purple to black and are very colorful. On their own, I find them rather one-dimensional in flavor, kind of sweet and watery, but their true value comes when mixed with other fruit. I no longer need to add sugar; they sweeten up the blueberries or strawberries or whatever so sugar is not needed or missed. They do sucker, so that's a consideration. I have a 120' line of them along the sidewalk. In bloom, they are a sight to behold! Of course, the birds love them, and I love seeing the birds enjoying them, and with so many, I have enough to feel generous!
Within that front bed, I also have jostaberry which has not started to produce yet; hopefully, this summer they will start. I believe that they taste more of the gooseberry and not the muskiness of the black currant. (It is a cross between black currant and gooseberry, thornless), clove currants (beautiful yellow flowers in spring that smell like cloves and then fruit is black. The shrub remains fairly small 4-6'? I also have other colored currants--white, red, black and pink, along with gooseberries and honeyberries. I did have some dwarf everbearing and Gerardi dwarf mulberries but was worried about the roots doing damage to the driveway, sidewalk or septic; I moved the four of them out back with some of the wilder looking things. Even though they are dwarf and the Gerardi only reaching 6' after ten years, when I checked with the people whom I bought them from, they, too, advised that I move them away. I have yet to taste them but people do go on about them, so I'm excited to taste them. While not a berry, I also have rhubarb in the front bed. I like it because the leaves are very dramatic, it stays put and is well-behaved and produces early in the season. I have small trees out there that will stay in the 10-20' range: quince, medlar and paw paw. I have some American persimmons, but they will get taller than that, but I was wondering if you could grow an Asian persimmon which stay rather small--the fruit is considered a berry, so that's why I put that in here.
So far, my favorite of those things mentioned would be the strawberries, with 2nd place being taken by the asparagus. Of course, the garden is going on its fourth year and I have yet to taste a lot of what is to come! I'm dying for the paw paws and persimmons to start fruiting...and the kiwi, hazelnuts, bush cherries and raspberries...That might be something you'd be interested in...I just discovered that there are thornless bush raspberries that only get to be about 2-3 foot tall and wide. I got them through Stark Bros. No crazy canes to deal with. They are called Bushel and Barrel Raspberry Shortcake.
https://www.starkbros.com/products/berry-plants/raspberry-plants/bushel-and-berry-raspberry-shortcake
I'm wanting well-behaved plants and ones that don't require a huge regimen of care and these fit the bill.