Ginger Beer - First Attempt

My first homebrewing attempt ever. One gallon batch of ginger beer. Recipe adapted from a give gallon recipe found on Homebrewtalk.com.

Tea:
1/2 lb ginger sliced on mandolin (managed to avoid adding blood though I did cut myself)
1/2 gallon water
Zest of 1 lemon
Zest of 1 lime
1/4 tsp cayenne pepper
1/4 tsp vanilla extract
2 cups brown sugar - added at end of boil

Process
Boiled tea for 15 mins then cooled for 2 hrs. Attempted to cool with lid on but temperature did not drop rapidly enough. Took lid off and crash cooled in fridge to get temperature down to less than 105F. Once cool, tea was added to sterilized gallon fermenter, straining out ginger and zest.

Added 1/4 cup lemon juice and 1/4 cup lime juice to fermenter. Added an additional 1/2 gallon of water, pouring it through filled strainer. Pitched ~1/3 tsp Red Star Champagne yeast with 1/4 cup water with water just below 105F. Stirred occasionally for 10 mins and then added yeast mixture to fermenter.

Original gravity = 1.033

Sealed and left to ferment for four days. Transferred to bottling bucket, then bottled.

Final gravity = 1.011, 3% ABV

Used plastic bottle to monitor pressure. Left in basement to pressurize. Transferred to refrigerator after about 10 hrs with plastic bottle being hard.

Result
Carbonation is low but there. Could have sat in basement for another day probably. Flavor is very dry with no sweetness whatsoever. Nice after burn. Best drunk chilled and in a chilled glass. The dryness can be offputting the first couple of swallows but the palate adjusts fairly rapidly.

Possible Adjustments
Backsweeten with non-fermentable sugar (splenda - maybe 1/3 c.)
Possibly add additional corn sugar to tea to give the yeast more toys
Ferment an additional day for a higher ABV
Possible soak of ginger in dark rum before adding to tea
Pasteurize rather than cold crash to stop ferment and allow longer aging.