You probably know this already but after adding calcium carbonate, the calcium tartrate can take a long time to precipitate out. Small adjustments may be better made with potassium carbonate, but this can raise the pH a lot more.
So in my opinion your wine may not be stable from a couple of points of view. First, you have unfermented sugar, both from backsweetening and from incomplete fermentation. Second, you may have calcium instability from the calcium carbonate. If you want to prevent fermentation of the remaining sugar, you need to stabilize with sorbate and sulfite (KMS or Campden). This sugar will offset the acidity to some degree. Knowing the TA will help address the taste problem. If you can get those numbers somehow, post them here.
One other thought, maybe there is something about late harvest Vignoles. In 2013 I made Vignoles - the numbers didn't look bad, looked like it should have made a decent wine - 3.04, 0.84%, 1.104. I never could get that wine balanced. Maybe too much alcohol. At that time the only tool in my toolbox was sugar, so that is what I tried, I also watered it back just a bit, but it was still overpowering and tart. My wife ended up using it in wine spritzers. I have two bottles left and it is probably past its prime but I'll crack one open tonight and see if time has helped any. I made 6 gallons this year from the same vineyard, but picked earlier. 2.85, 1.5%(!), 1.086. I adjusted preferment with calcium carbonate, fermented it VERY COOL with QA 23, and I swear if you stuck your nose in a glass right now you couldn't tell it from a NZ Sauv Blanc.