You might get lucky with a $300 new bike, but I ind of doubt it. If you don`t mind going with a used bike, there`d be no problem getting a good one for that price. Do you actually dislike your current bike, or you`re just considering?
About downhill speed, I think you`re right. I won`t go into the uphill stuff because since you already have a heavy bike, you probably already knew what the other guys just said
. Also, I suggest not being overly concerned about weight of a commuting bike.