Some ginger beers are fermented with a ginger bug or a combination of brewer's yeast and lactobacillus. Depending on what bacteria can be co-resident with the yeast, acidity can happen. Lacto should produce a "lemony" acidity. Kombucha and some wild fermentations can also have acetobacter, which produces a vinegar taste. The type of sugar won't have a large impact on flavor, especially in the presence of strong flavors from lacto or acetobacter or the ginger itself. In a "normal" fermentation (one where bacteria is kept at a minimum), sugar just ferments out and produces alcohol, but some sugars are harder to consume by some yeast, leaving some residual sweetness and flavor. Is the "face-melting acid" flavor like lemonade or like vinegar or something else? I suspect the acidity is due to fermentation characteristics (like bacteria) rather than the type of sugar used, but it's a bit hard to tell without more information. In a sour-style beers, yeasts (like Brett) or lacto or other sour bacteria will consume the remaining sugars after the primary yeast has finished, getting more sour over long periods of time.
I was checking in on a sour mash this morning and a couple of things occurred to me. In a sour mash, you are attempting to control what bacteria grows by controlling the temperature. Acetobacter; the vinegar component in the Ginger Plant inoculation, grows best at around 77-86 F (25-30C). By lowering the fermentation temperature you could limit the bacteria production and favor the yeast. I sort of like doing the opposite with Kombucha (ferment with a brewbelt to keep it at 78+F to favor the acidity and ferment for longer).
Also, if you are re-using your culture (GBP), the culture will change composition over time to favor the conditions, so the vinegar taste (acetobacter to yeast ratio) would be enhanced over generations by using higher fermentation temperatures. By the same token, using a lower fermentation temperature and harvesting, you will discourage the acetobacter population (raise the yeast to acetobacter ratio) in the culture over time, producing a more neutral flavor.