According to THIS CHART
you're brine time was just fine. I usually shoot for 8 hours, but have done as little as 5 hours with good results.
As said, if you let the bird rest uncovered in the fridge for a while it will help dehydrate the skin. The "tough or rubbery skin" thing is the one and only down side with brining, but it can be addressed.
Glad it worked out for you. Sounds like it was a hit with the family. Given the time (which I almost always allow for) brining is the ONLY way I'll cook chickens, whether in parts, whole or even just wings. Brining makes PERFECT wings.