Hi sidthekid, Welcome. I don't use cinnamon or nutmeg so I am no expert but those quantities seem like a lot for 3 gallons... But if you have a tried and tested recipe I won't argue - though IMO, many recipes offered as "tried and true" are either not tried and if tried tend to be duds... But be that as it may...
Why the sugar? Mead (honey wine) or cyser (honey wine made using apple juice rather than water to dilute the honey to a fermentable level) don't need additional sugar.. An appropriate WINE yeast will ferment dry every last gram of sugar in the honey and the apple juice.. So any added sugar will affect the flavor - not the sweetness...
Now you should get a specific gravity of about 1.045 (or thereabouts) from the apple juice and about 1.040 from each pound of honey when dissolved in a gallon of water - so you are looking at the equivalent of about 3 lbs of fermentable sugar in each gallon (a gravity of about 1.120) WITHOUT any added brown sugar (the brown color comes from added molasses)... A gravity of about 1.120 has the potential to ferment out to about 15.5 % alcohol by volume... If it ferments completely...
I would look for some nutrient for this mead. There is a lot of sugar for the yeast to handle in the first hours and days of the fermentation...
You might need to sweeten this cyser before you bottle it - so check out how to stabilize wine with K-meta and k-sorbate. then add either some apple juice concentrate to sweeten or more of the same kind of honey...
Good luck!