Having just finished my second batch of cider, I'm guessing the key to being able to drink it quicker is using a cider or ale yeast (somebody back me up if they have found this to be the case or not). I basically used the same process you did, including back sweetening with some apple/razz concentrate and it just tastes sour and yeasty as hell. Both times I have used a champagne yeast because the guy at my HBS said that was really the best choice for making cider. Perhaps it is, but you have to let it sit at least 3 weeks after primary before it is something you can begin to enjoy drinking.
I'm going to make a bigger batch this time and try an ale or cider yeast instead. Hoping I can enjoy this batch two weeks after starting this way. From what I can tell, the champagne yeast will yield a higher final ABV, but until I'm sitting on some finished cider I can enjoy in the meantime, the waiting is just too much (I have heard it is the hardest part).