I made dill pickles using an old Ukrainian recipe fermenting the cucumbers in salt water. I wanted to can them when they were finished instead of keeping 10lbs of fermented pickles in my refrigerator. I didn't want to use the salt brine the pickles fermented in,so I made a brine using 1qt white vinegar, 3tbls salt, 1tsp mustard seed,and 1/2 cup sugar. The result is really, really sour pickles! Can I open the jars and dump the brine and use salted water as canning liquid? Or what can I use?
If you are going to do anything, do it when you are ready to put the pickles in the fridge again, not when canning - acid keeps the canned pickles safe.
So - leave them really sour as canned. When ready to eat a jar, open, dump the brine, add water (whether or not you salt it is up to you and the salt level in the pickles - I'd try plain water) - put it in the fridge. You might want to let that soak for a day or two, and you might want to dump it again and replace it again, depending on how things taste at that point.
Traditional preserving methods may in fact be too intense for eating as-is, and this is not always a matter of what you are used to. I recall reading a story set in the 1800’s, and noted details of preparing dinner: salted meat was left to soak in the morning to cook that evening. The salt and dessication was a practical preservative and something to deal with, not part of the intended flavor.
I made sausage with a recipe said to be the favorite of Chopin, and it was far too salty to eat—comparing other period recipies, I noted they generally had about triple the salt of a modern form.
The same might be true of your canning method. The acid preserves the fruit without modern refrigeration etc. and maybe they didn’t eat them out of the jar. Maybe they added them to dishes where the intensity would be diluted by the entire recipe; maybe there was a process you don't know about like replacing the liquid after the jar is taken from long-term storage and opened for use.
That would be my guess: you rince and replace the liquid after opening the can.
The real tradition may have kept the original brine (or fresh brine without the fermentation products) in a barrel that was not what we consider to be hermetically sealed. So you're mixing two different techniques, and they may have interacted in ways not intended.
The sugar in your brine is probably not for any sweetness of flavor but as another dessicant. Note that white sugar would ot have been available before the 18th century so that’s not authentic (or not that old). To reduce the sourness, consider baking soda to actually cancel the acidity.
You need the acid for preservation, I'd suggest adding more sugar to the mix to balance the acid flavor. You won't be reducing the acid so you will still have the preservation, but it may work to make them more palatable. I'd experiment on one jar first to see. You could do this before canning, or you could mix in after opening.