Yep. That was one of the first things I did after setting it up was update the firmware. It was a relatively large update, too. I just checked again for the hell of it, and it's up to date.
I tried turning WiFi sleep on, so WiFi isn't active when the screen is off. This seemed to help a little, but it's still pulling way too much juice for my liking.
Yeah, now I remember you can run through the update in the set up screen, and it takes forevvvver.
I don't think you should have to turn WiFi sleep on to keep your battery usage down. As I said I am using ~1% per hour today with minimal usage but I do not shut my WiFi off at all while I am at home. It sounds almost like your phone is fighting to stay connected to the router. I used to run WPA2 for my security until I had a little disagreement with it and my Linux system and the Linux system won out so I dropped it to WPA. That may be another area you might want to look at, if you're comfortable with it.
As far as having your router to run at the 300mbps limit you would have to have all of your peripherals compliant with the 5ghz bandwidth. Which, unfortunately for us Fascinate owners is not a possibility once we connect our phone. So you might also try changing some of the settings for that to see if it helps.
One other thing, I don't know if you have an option for the Channel Width but check to see what it is set for if you do.
I wouldn't worry so much about the actual Channel that is more for issues with connectivity. For instance if someone around has their on the same channel as you are you would want to change your channel.