I use the exact same technique, I set my manual height to 768, and it works fine across ANY mobile/tablet resolution. The only thing is that I have a little more space on the sides of some devices (depending on the aspect ratio).
And for this, the only thing you need to take care of, is having a "big" background image, having something tilable for example, or just a 3 of the same backgrounds that repeats (you add one to the left of the one in the middle, and one to the right).
You see ?