Thanks for pointing me to Crabbies. I wasn't aware of any alcoholic ginger beer in the US. I've been playing with a sessionable (read: 3.5%ish) ginger beer. It's pretty tasty, and makes the best Moscow Mule I've ever tasted, hands down. Here's my recipe, taken from the 'Ginger "Beer" (with wine yeast)' thread.
1. Mix 3 lbs high quality ginger into 2.5 gallons water (I do it in batches in the blender)
2. Add 10 cups turbinado sugar, or 8 c turb, 2 brown sugar. Generally, 2 cups/gallon is mildly sweet. I usually add a few squirts of honey to the boil as well. A little honey goes a long way in this recipe, btw.
3. Add 1/4 tsp of cayenne pepper for a kick if you want it, pinches of sea salt and other spices. I've been adding 1 tsp cream of tartar, but I don't think that's needed after reading through threads here.
4. Boil all that for 15 minutes, then cool for 120. Strain, Transfer to fermenter, double the water, and add 1 cup each of lemon and lime juice. Add yeast (Red Star Champagne Yeast) when temp is right (I shoot for 101). Usually OG is around 1.044 here.
5. Ferment for 48 hours (stirring/aerating regularly) for "Ginger Ale" at around 1.3% ABV, or 96 hours for about 3.3%. Go longer for stronger.
I haven't yet tried to fully ferment and adding late sugar yet. Alcoholic potency isn't my primary goal. 3.3 sessionable is.
6. Here is where I would advise to bottle pressurize for 24-48 hours, but since you're kegging, just keg that, leaving as much sediment on the bottom as possible. A little doesn't hurt, of course.