I make blackberry wine every year with good results (lots of bushes near by). I only use fresh berries (rather, berries i picked and froze, or fresh; either way, only berries i picked). When i've bought frozen berries, i've noticed a considerable taste difference. Part of this is attributable to the breed of black berry, as most frozen berries for purchase from the store come from farms in the south, if i remember correctly (i'm in the pac nw). Part of it is also that the berries I use are really ripe. So, probably the sour taste is just that the berries fermented out all the way, coupled with the inherent flavor of the store-bought berries picked at sub optimal sweetness.
So, what i'd suggest you do is make a gallon of banana wine, and get some wine conditioner. The banana wine, made with about 5 pounds of bananas per gallon, along with about 2 pounds (4-ish cups) of sugar per gallon, can be blended with the blackberry wine sparingly. It'll add body and sweetness, but the flavor of the banana will be lost to the blackberries. blend a small amount til you have the body and mouth feel you like, then scale that up to your entire gallon of blackberry wine.
Then, when that's done, buy some of that 'wine conditioner' and sweeten the wine with it to taste. Or, use potassium sorbate and sugar. Either way, coupling the back-sweetening with the banana wine blending will go a long ways to making that blackberry wine rich and flavorful.
my two cents.