Formula for Calculating FG from Refractometer?

I use a refractometer for brewing (so far just small mead and cider) that gives readings in degrees brix, and it was pointed out recently that refractometers don't give accurate readings for final gravity because the alcohol content skews the reading.

Can this be corrected accurately without buying a hydrometer? What formula should I use?

So far, I've been using the following formulae from the depths of the internet to calculate alcohol quantity (source linked):

{Brix/(258.6-([Brix/258.2]*227.1)}+1 = Specific gravity

% Alcohol = ((1.05 x (OG – TG)) / TG) / 0.79

So, for example, one gallon of cider started at 11.8 degrees Brix and finished at an apparent 4.1 degrees, which if read literally is just under 4% ABV, but tasted stronger than that...