Glad it's working out for you. I bet your new one will be must better. As far as testing - I tried to mimic a test from an endgadget review.
"When it comes to battery life Amazon says you can expect 11 hours of normal usage, and in our typical battery rundown test (with a looping video, WiFi on and the display set to a fixed brightness) we scored about an hour short of that."
I don't think they are streaming video, and they don't say what "fixed brightness" they used.
I have some purchased videos in the Amazon Video on Demand store. I downloaded the longest one to my fire HD. Once fully charged I set the brightness to the middle (this was arbitrary on my part) and I started playing the downloaded video - any time I thought about it I restarted at the beginning (my poor man's looped video.) With my replacement my play time was in the right ballpark for the 9" version - the same endgaget test yielded ~9 hours for the 9". My the one I replaced couldn't make it past 5 hours.