Have you racked it into a carboy since it finished fermenting? Get that done ASAP What size is that batch? 2 or 3 gallons?? Remember to add the K-meta /Campden tab(s) at the standard rate of 1/4 tsp per 5 gallons or 1 tablet per gallon.
Also, is there a recycling center near you?
OR do you have some glass jugs like a 1/2 gallon one that has the same size opening as a one gallon jug(carboy) I find all sizes of glass bottles at our local recycling center. Many have the same size thread as a standard one gallon carboy.
For example - Yesterday I racked 2 gallons (2 carboys) of a Peach-Riesling batch into the following containers
1 gallon,
1/2 gallon
1.5 liter container.
All are glass and have airlocks on them.
Unfortunately.... there was about 10 oz of cloudy 'dregs' at the bottom of those two original carboys. (That's why I downsized the containers) Soooo I took those dregs and put them in another 16 oz container and popped it into the fridge. Last night we had that after supper. Wife decided she would like it sweetened up a bit - too dry for her.
Sooo you do have that option of downsizing if you have some airlockable glass containers. As someone else mentioned if you have those drilled stoppers like this one, they can be turned upside down on a wine bottle to seal it... OR you can simply 'steal' an oz of wine to taste. You can even use cleaned wine bottles for aging with that stopper(bung) upside down on it. Just be sure to sanitize them before using.
As for sweetening up the wine. Make up a simply syrup of 2 cups sugar to 1 cup hot water. You can force it to a 3 to one or even 4 to 1 if you want to take the time. Most of us here seem to use 2 to1 rations.
Then take 8oz (1 cup) of your wine and start with a small amount of the simple syrup. I have used plastic syringes and started with about 5 ml for 8oz of wine. Stir and taste. You can continue with that until you are almost where you like it. Stop a little short of perfect because as the wine ages and loses that sharpness, you might find it slightly too sweet.
Anyway that's one way to have something now and of course learn how much to sweeten the rest. Most times I end up adding about 1/4 oz per cup of wine. Of course the math then is to take the remaining amount (ozs) divided by 8 and that result times the amount of simple syrup you used to get the right sweetness. (Hope that isn't to confusing.)
Here's a typical outcome for me.
Simple Syrup needed 1/4 oz (.25oz) per 8 ozs,
I used 8 ozs (1 cup) of my gallon (128 oz) (16 cups)
So I have to sweeten now 15 cups (120 oz)
15 x .25 = 3.75 oz of simple syrup to add to the remaining wine.
ONE BIG THING TO REMEMBER. The wine can restart fermentation if not treated with Potassium Sorbate and K-Meta at least a couple of days before you back-sweeten the finished wine.
So if the wine clears quickly, and blackberry seems to be one that does clear quickly, once it's clear you can do that downsizing of containers. As someone else mentioned since you boiled that juice it may be slower to clear and may need another dose of Pectic Enzyme to help it along. BUT for your tasting your samples don't have to be clear.
I normally lose some volume in each racking with the most happening in that first racking. Since I know I am going to lose volume, I normally start with extra volume and extra fruit and aim at a slightly higher ABV than I want. (Aim at 14.5% for example) Then as I have to top off the container for my missing volume I'm not diluting it significantly. If my recipe called for say 5 lbs of fruit and I actually use 5.5 lbs then a little water is not going to ruin the taste. My ABV is still going to remain above 10% and that's the minimum you want for a wine.
By the way if you get it too sweet you can always double your sample size and adjust the amounts from there. So if you had added 1/2 oz of simple syrup and found that too sweet, you could add another 8oz of wine and that would make your bring your rate back to 1/4 oz per 8ozs.
Hope the math juggling for the back sweetening isn't too confusing.