How can I ascertain ABV and/or Brix of a mixed fermentation using only specific gravity measurements?

I recently bought an inexpensive little hydrometer in the goal of roughly measuring the alcohol and sugar content of my home-brewed kombucha. I didn't think too hard about the methodology of this process until it actually came with its instructions. In the end (if I understand it correctly), it seems that the process of estimating alcohol/sugar content via comparison of starting and ending specific gravities operates under the following idealized assumptions:

1. The starting measurement deviates from a specific gravity of 1.00 only to the extent that your starting liquid contains pure sucrose;
2. The ending liquid (from which you take the ending measurement) deviates from the starting liquid only to the extent that a portion of the starting liquid's sucrose was converted into alcohol.

Regarding kombucha, I expect (1) is violated by the fact that a brew prior to first fermentation is—beyond sucrose—composed of a decent amount of the byproducts of brewed tea leaves, and also starter kombucha liquid, plus whatever not-pure-sucrose ingredients you add before 2F. But of more concern is the fact that the fermented alcohol in kombucha is largely converted into acetic acid, completely violating (2).

If I assume the violation of (1) is of minor consequence, then I'm thinking that the process could still be salvaged: We can assume we start out with a pure sucrose solution, some unknown amount of which gets converted into some unknown proportion of alcohol and acetic acid. But, that link above provides a means of measuring the exact amount of alcohol. So, if we know the specific gravities of pure sucrose, pure acetic acid, and pure alcohol, and we know the specific gravity of the starting liquid, ending liquid, plus how much alcohol is left in the end, we should be able to mathematically solve for the three unknown quantities (since we will have deduced three linear constraints).

Am I mistaken or overthinking any point of this? Is there an easier established way of estimating these things for kombucha?